Disclaimer: I am not a psychologist, nor a scholar on this subject matter. I encourage all to do their own research and come to educated conclusions. I will give some suggestions at the end of this post. (The Wiki link below has more scholarly reading than online sources, if you are so inclined.)
First of all, I want to clarify the difference between the two terms sensitive and empath.
HSP is the term (popularized in the mid-1990s) describing a person who is aware of the subtleties in their environment and can be easily overwhelmed or overstimulated in certain situations, such as crowds, emotionally charged situations, or have a extraordinary sensitivity to sounds, smells, touch or textures, or tastes. This is not to be confused with a sensory disorder - HSPs are simply extremely aware and regularly deal with over-stimulation through avoidance or adaptation. They also can do what has been termed 'sponging' of the emotional state of those close-by, even strangers. This is where it can get tricky, because Empaths are those who intuitively know the emotional state of those close-by, and in some cases, those far from them. I like the succinct wiki definition: "being an empath is when you are affected by other people's energies, and have an innate ability to intuitively feel and perceive others. Your life is unconsciously influenced by others' desires, wishes, thoughts, and moods. Being an empath is much more than being highly sensitive and it is not just limited to emotions."
I do believe that sensitivity is passed from parent to child, I have observed that all three of my children exhibit sensitivity, albeit different in all three, and in varying degrees. I also believe that my own mother was a sensitive in the above definition.
As you can see from above, there is definitely some overlap, which can make it quite confusing. In my opinion, the major difference would be the level of compassion. An empath is definitely compelled to feel, and even take on, the burdens, pains, and drama/trauma of others, where as an sensitive mostly aware and may sponge those feelings of others, but may not feel quite so compelled to action. This is not a measurement of the goodness or righteousness of a person, it just is what it is. The focus of the sensitive is the awareness of the feelings around them (or stimulation), while the empath's focus is on where is it and what needs to be done to alleviate the suffering.
I was not aware of my own situation in such terms for the majority of my life, however, I have always lived by my intuition. I not only feel my own feelings, and those around me, but I know things.
Kind of like the old term ESP (extra-sensory perception) from back in the day - I 'see' people. I see their heart, I feel their spirit. I know immediately if they are lying, or being manipulative.
I oftentimes know when someone is thinking about me, or is about to send me a message. I also can predict what a person will say within a conversation, or how they will react to certain things.
I can always see all sides of an argument, and the motivations of those involved - and further, I have compassion for all sides, too.
I am hyper-sensitive of all the details of a space, whether it be at home, a restaurant, or classroom - and I know what needs to be done to make everyone the most comfortable. A sensitive will insist on straightening the crooked picture hanging on the wall; an empath will feel all the people in the room and understand the nature of relationships.
I instantly know if someone is being confrontational with me, even if just for sport, and it sends me in a spin. When I am angry at someone, I cannot say things that will hurt their spirit, as I don't want to implant 'recordings' in their psyche that will repeat later. I am only confrontational if I absolutely have to be, and it makes me pretty angry if I have to go there. (That is not to say that I haven't hurt people - I know I have. It is just that I live with their hurt every day - their hurt is my hurt, too. And worse, I caused it. This is exactly why I don't try to hurt anyone.)
I believe people of all ages are ageless inside of themselves, thus deal equally and respectfully with all ages. Babies are attracted to me, and I to them - we 'see' into each other. Children feel the protector in me, and I will have complete strangers share intimate things about themselves or their lives with me.
I feel love and compassion for people, especially those who I have had close relationship with; they are forever with me, even if the relationships have been long extinguished. The exception would only be those who have decided to be hurtful to others due to greed or selfishness, especially repeatedly. And even then, I cannot hate them. I strongly believe that everyone has a right to their opinion and I will defend that right even when I don't agree.
As far as my sensitive side, I hear everything. A pencil of the students around me rasping on their notepads, the clock ticking, and the person walking down the hall. I hear the cars go by on the street and the conversations or television shows of the neighbors. Other people can hear these things, too, but for them it is not a distraction or even noted. I can hear the chewing of the people in the next restaurant booth, or the conversations happening back in the kitchen. Yeah, they are all acknowledged in some way in my crazy brain. Just recently, I was glad a couple of sweet ladies decided to leave the restaurant because one of them kept playing with her car keys in her pocket. They were sitting three booths away from us.
This is the life of this sensitive-empath. Yes, one can be both. I am highly sensitive, but not to the same extent that I am an empath. Frankly, I think both work together, and placed inside the personality of an INFJ, that is some kind of powerful intuition. And a lot of input to sort through constantly.
This ability to know makes people uncomfortable. So, I spend my life pretending I don't know things. I let them tell me. Often they don't, and for the bulk of my life, this caused quite a bit of problems. People don't often want to be 'seen.' I can understand that. I don't have any idea what it would feel like to have someone 'see' me in that way. I have never been in the presence of another empath. But, if I was, we would both know it!
Dr. Aron has spent many years now researching sensitives, and has written this wonderful book about the subject. It actually was our first exposure to this understanding of sensitive people, and it was a huge help in the journey to understanding. I am extremely fortunate to have a partner who is completely committed to helping me navigate through my world without over-stimulation. For a sensitive, much less an empath, this is extremely important. However, even before I knew anything about sensitives, I had adopted some adaptations to help cope. I eliminated television watching, especially the news, I started being very choosy about the movies and entertainment I would watch, and I attempted to protect myself in a religious context. Some of those things were beneficial, some not so much. Sensitives often adopt behaviors, such as that of introverts, in order to cope with over-stimulation. That is not to say that they don't like to socialize or be in stimulating situations, but that they need to allow time before and after the stimulation to not only debrief, but recharge and ground themselves again (somewhat similar to introverts). Enduring over-stimulation on a constant basis causes fatigue, illness, or melancholy/depression in body and mind, somewhat like a two-year old that has just had enough.
A couple of things that Dr. Aron uses as indicators are difficulty in decision-making and the tendency towards addiction. I don't seem to have those two tendencies, however I can see where she is deriving those conclusions. When one has so much informational input, it may be difficult in deciding the best course or choice. Similarly, unconsciously seeking comfort could lead one down a road of addiction, especially alcohol or other sedative-type drugs. While I am not technically addicted, I spent many years using sleep aids in order to make the world go away. Perhaps my upbringing contributed to my awareness of both of those issues - my parents were excellent decision-makers and modeled the behavior clearly and often, however there was alcoholism in my family, as well. I knew that I never wanted to go down that path, hence a stubborn moderation of my own use of recreational drugs. Thankfully, I have been pretty successful in both those areas as I am efficient with decision-making and am not an alcoholic!
So, how does this play out in my life on a daily basis? Well, I have very few close friends, but the ones I have are very aware and used to dealing with my 'knowing' and 'feeling.' I have lost a good many friends over the years, and it is usually due to their discomfort or misunderstanding (I don't think I am an easy friend to have - I expect so much of them because I expect so much of myself.) Sometimes I feel compelled to confront concerning dishonesty - that never goes over well, and is such a bummer. Or if a friend is stubbornly holds an identity of themselves that differs from how I 'see' them. That kind of naked honesty is always difficult, and typically the relationship just goes away, or it is easier to just not be close friends. I have a lot of acquaintances, and that is OK, too.
I have to be careful with facebook or other social media, because my sensitive self can get pretty bruised up if I am on there too much. I tend to post things about social issues close to my heart like gender equality and charity/compassion for the underprivileged. I often hide those posts or people who post a lot of manipulative religious or political messages because I see the motivation behind them, and it is not always healthy or true (to my way of thinking). All this is a way to protect myself from over-stimulation and emotional battering.
I am a student, which can be quite a challenge (as noted above) - I sense everything! I sense the self-doubt of myself and other students, or worse the over-confidence that sometimes doesn't go well. I have deep compassion for struggling students, and often end up with those in my study groups. I hold myself to a very high standard, and often develop respectful and interesting relationships with my profs (since they are closer to my age than the rest of the students). Yes, I sense and 'see' the profs, too. The classroom is a cacophony of input for me, and is usually a real challenge.
Actually, life itself is a challenge for a sensitive/empath person in ways that others don't seem to have to deal with. Just having a conversation with someone can be an exercise of juggling what they are saying, what you feel they are 'feeling,' and how you 'know' they are perceiving what you are saying. But, if you have a sensitive/empath in your life, you can feel comforted that they may know and understand you in ways others just can't. It has been called a gift, and oftentimes I feel like it is a curse, but mostly I call it my superpower. Just like any superhero, their powers are both within and outside their control. I often wonder what it would feel like not to feel, but then I realize how awful it would be if I suddenly couldn't feel others around me. It would be like a Jedi suddenly stripped of force-sensitivity, or Superman in the presence of kryptonite. I rely on my ability to feel in order to move through life, as I know it.
I hope this has helped clarify things a bit, even if it is only my lay-person perspective. I am open to comments and discourse concerning these things, if you so choose. As promised, below are a few links you may find helpful if you are looking for more information.