Well I don't KNOW even in a state of uncertainty --- and I suppose it is going to be up to you to pursue it .. or someone else might stumble over it .... I would say, though, if you have documents one of which says Annie Mae and the other says Frances Ann, then you have a man who had two marriages ...
If you have only two census, one of which says Annie and the other says Frannie, again it is possible there was two marriages ...
You really need to chase down the documentation on the man, his residence & year starting with birth and ending at death ... somewhere in that time frame he married the once and maybe twice ... you might uncover even a 3rd marriage and the locale and date of each marriage is listed under "residence" (at least on that one day)
You can take an alternative route by tracking down each child's death records to see whether their mother's name appears on it and if so what name was it?
I usually do both routes, and my 3rd is to track the same for the wife or wives ... everyone gets sifted