what is the difference between a fake bill and a counterfeit bill?

Answer 1

A 'fake' bill does not necessarily have to look real, like monopoly money. A 'counterfit' bill is made specifically to pass as a real bill.

Answer 2

Fake bills are like the ones you buy at a toy store or like the ones that come in Monopoly which are legal to produce, but have NO value... but a counterfeit bill is one that is ILLEGAL to produce, because it is for the sole purpose of passing off as a REAL piece of LEGAL currency and also has NO value.