I have wondered about this as well. One of my best friends is also INFJ, but she is more like you describe yourself than the first type you describe, which is more like me. I've wondered if that has something to do with some sort of level of development in afterlife, etc. but probably just my overactive imagination having fun with me.
I think MAYBE it has to do with upbringing? My mom is a Te -- very rational, very non-emotional, and I grew up with her as my primary role model, so I may have adopted some Rational traits in addition to my sensitivities. I certainly use Fe (always thinking about others, wanting their approval, not wanting to disappoint them, keeping them happy, avoiding conflict, acting as a peacemaker -- heck, I even let our DOG choose where HE wants to walk, and I go home early if I think he's getting too hot) but I can also "detach" from people and things. I'm way more analytical than a lot of my friends. I can come up with rational reasons for most of my arguments. They might be Fe-leaning, but I can back them up.
But, some of the INFJ Empath tropes, I just don't get. Like... not wanting to buy furniture because you get "vibes" off it from the previous owner? WHAT?? I never think about the people who owned antique furniture! I choose not to purchase most antiques because I like NEW things; it has nothing to do with vibes, and a lot to do with my inferior Se wanting furniture that isn't scratched, dented, or worn in places. My reaction isn't "emotional" in that sense -- it's based on aesthetic appearances and practicality (can I afford it? does it match my other things? do I like it? where would I put it?). Or... not wanting to eat meat because you can "feel" the agony of the animal? I don't like meat, because I know where it came from, but I can still eat it because I choose NOT to think about where it came from.
Television wise -- I often like very dark, emotionally deep stuff. I don't mind violence (heck, I even watch
Hannibal) but I don't like torture or cruelty.
Some emotions, I can't turn off -- any animal abuse horror story I have ever heard, I have to work hard not to think about. But in dealing with people, I can choose to step back and say, "Stop emotionally engaging." I FEEL for them, but I can also just... stop caring and walk away.