I support a merge and propose to keep enumerative-combinatorics. I would not even keep enumeration as a synonym.
You should have been able to propose a synonym though (but only in one direction and maybe you only tried the other); one needs some score, five IIRC, in the tag for this. But anyway that system does not work so well, and one needs to post on meta regardless.
On the side question: no, this is different and both can happen without the other.
A synonym only is active for future usage of the tag. Attempted usages of the minor tag after the synonym was created are mapped to the major tag. But legacy usage is preserved. In particular, if the synonym is canceled the situation before the synonym is restored. (Yet the two tags are taken together for searches so they nevertheless operate as a joint tag in a way as long as the synonym is active).
By contrast a merge will instantly retag everything and the minor tag will cease to exist, and this is essentially irreversible (and thus reserved to moderators). One can create a synonym directly as part of the merge, but this is optional.