tax exemptions/credits does anybody know the difference?

I find myself in the impossible situation of fighting with my ex over who should be able to claim the kids for tax purposes! I say that I should be able to as he only has them 4 days out of the month and only pays child support when he feels like it!

He says that he should be able to claim exemptions and I should be able to claim credits.

Does anybody out there know the difference and what I should do?

I don't want to sign my life away!

Jenny