The 3 main province at civil war in the south seem to consider themselves Muslim rather than Thai.

Wit marriages, do they have the same wedding legally as the rest of the country?

Yes, a legal marriage is nothing more (or less) then registering you are married at the local amphur by signing the marriage register.

A marriage ceremony, which is not a legal marriage, and simply a private affair wil be different for a muslim, bhudist or christian.

Of course, it is Thailand!