I understand how people are feeling - I rarely "feel" or "experience" how other people are feeling. I can and do put myself in other people's shoes, but it's not something I do instinctively, whereas understanding how people feel and where they are coming from is. That being said, I don't think I'm overly sympathetic. I definitely have the capacity for great sympathy, I'm just... less likely to give it to just anyone? Lol, and I don't mean to sound like I'm stingy with my sympathy. This sounds terrible - I'm really not sure how to put it.
That being said, I don't think empathy is highly type related. Any healthy individual has the capacity for empathy and tbh I don't see the point in over-analyzing it.
How is this empathy? Understanding and "feeling" how someone else is feeling is empathy. Adopting their feelings as your own is not empathy, lol. If anything it shows a weak understanding of your own feelings and and an inability to be assert them when necessary.
I think you are taking this whole being empathetic thing a little too far.