There is certainly some overlap, but are the two words technically interchangeable?
Someone who is egotistical is egocentric; someone who is egocentric may or may not be egotistical.
Egocentric people think primarily of themselves; they are the center of their own worlds, and little else has relevance.
Egotistical people also think primarily of themselves, but have the additional tendency to think only good things about themselves.
Someone could be both egocentric and self-loathing, self-obsessed and self-despising; many people with clinical depression, for instance, can be described in just that way.
Being egotistical and self-loathing in the same moment, on the other hand, is harder to imagine, though someone could certainly vacillate between the two states.
"Egotistical" means to think very highly of one's self, usually understood to mean unrealistically highly. "Egocentric" means to think only of one's own problems or concerns, or someone who doesn't care about other people.
They're certainly related, as someone who thinks he's the most important person in the world would presumably think that his well-being is the most important thing in the world. And the kind of personality that would be one is likely to be the other.
But they're not really synonomous. You could have a very realistic appraisal of your own strengths and weaknesses, and still be worried only about your self. Or on the flip side, you could think you're the most amazing person who has ever lived, and then conclude that this means you have a responsibility to help all those less able than yourself and be very self-sacrificing.
There is actually another difference. I just cant recall which one is which and I've been searching online so I was led to this page.
One has a definition of something like viewing others based on the self. Let's say it's the egocentrics who are like that. So while an egotist thinks only of himself, an egocentric can also think about other issues or other person but how he views these things is largely based on how he sees himself or as if the world revolves around him. Given that, kids are egocentric in that the only opinion about the world that they have is that of their own and they think everyone is thinking the same way. If I remember it right, they grow out of it after toddler years (maybe it lingers on some ;) ).
If you say, "well I get this concept" and then you think it would be easy for others to understand the same (because you were able to and it was easy for you to do so) then that's being egocentric. An egotist on the other hand would say "Piece of cake. I'm too good for this shit" and stops there.
The overlap I think is because both thinks highly of themselves.