Both of these are to be found in the science fiction genre. And in real life there are quite a few who identify as empaths, they feel what another person is going through. The extent of that feeling may vary. There are others who lack empathy altogether. I myself have a fair degree of empathy. Empathy can be painful and disturbing. It can be difficult to switch off. Apart from stage magicians there are not so many who identify as telepaths.
Should the latter exist it has implications. No longer are our secret thoughts and desires hidden. No longer can we hoodwink others and if they are a transmitting telepath like Charles Xavier, they can implant thoughts into our minds. In his case he can control it. To imagine that all our cunning plans lay transparent and that our hidden desires can be read, is for some a scary thing. You may have had a sexual fantasy and the object of that fantasy has read your desire at a distance. This idea could make you blush. This fear is especially so for those keen on manipulation, which often requires secret shenanigans. It is a sobering thought that if you have been up to no good, a telepath has known all along what you have been up to. You might lie to them in a bare faced manner and they have read you like a book. So, no matter how much you verbally protest they know your motivations.
If they are a projecting telepath they may be seeding thoughts into your head. Obviously, this kind of science-fiction skill is open to much abuse. But I suspect that those with such a skill would not use it thus, ethics perhaps being an enabler for this capability.
The Tibetan previously discusses these abilities as incoming for humanity, they are to be developed further as humanity evolves. The “mutants” may be become the new normal. Maybe science fiction is partially prophetic, maybe not.
If you are open to the idea of empaths and telepaths it would be interesting if you met someone with this especially if you had the same or similar ability. You could have a lot of fun, trying to see what worked and what didn’t. But most of all you would need to respect each other’s privacy from time to time.