True, but:
1. deposit can be any amount of money, not necessarily an advance
2. the down payment is usually followed by a loan
3. advance payment = the part of a contractually due sum that is paid in advance, while the balance will only follow after receipt on the counterpart in goods or services
http://en.wikipedia.org/wiki/Advance_payment
I know, but a deposit could be an advance; I understand very well the differences between those three notions.
Anyway, for things to be clear, I've placed in the comment's field an explanation. If it's not enough, I'll choose something else, even if I don't think it's wrong, in order to avoid a long discussion about one word.