What are the best pianos for practice and for performance, and why is there a difference?

The difference would be in the sound, the budget and the taste.

Any good old piano,  upright,  grand or electronic (with 88 weighted keys) will do for practice. I have plenty of students that do just that and it works great.

But I advise a good grand piano for performance if you can afford one. First off,  the sound will fill the room and let the audience appreciate the true musicianship of the player (s). Second,  there’s a comfort,  a touch, a response that only a good grand piano can provide.  Third,  this is a social occasion and it requires a little pomp.  And,  last but not least,  it looks great.