There are some slight differences. There are some common phrases: on the whole, as a whole, where you couldn't use entire. Also, in business we say "a wholly owned subsidiary of..." but we don't use entirely.
You can also say "that's a whole other story". You couldn't say " that's an entire other story". Though you could say "thats an entirely different story" Also, if you want to sound really American, you can say "that's a whole nother story" which is wrong: nother isn't a word. I think it comes from shirtening " That's wholly another story" but that's just a guess.