My spouse & I lived in 2 separate states all year. Both kids live with me, but I pay childcare for one, and spouse pays for the other. Can we both claim 1 child each?

Not sure what the difference is between claiming Child Care Credit and claiming a dependent... Since spouse pays for childcare for 1 child, can he claim that 1 child on his MFS state return and I claim the other?  We are trying to file separate state taxes, but already filed both kids together on our MFJ federal return.