If a man has a child with another woman while still married to his first wife, how would the child refer to the wife? Stepmother or is that only for births occurring prior to a parent marrying a non-parent?
This is one hundred percent an opinion. It depends on how that child feels around his fathers new lover, it doesn't matter if it is religiously or traditionally correct to be known as a specific label.
a woman who has married one's father after the death or divorce of one's mother
Allow me to offer a hypothesis (and do correct me if I'm wrong):
The word "stepmother" dates back to Old English, i.e. an epoch when the idea of getting a divorce was unthinkable, or at least extremely problematic. The original mother of the child would have to be a witch or something, in which case she would have been "dead to us."
Today, a woman is only seriously (i.e. not ironically or sarcastically) referred to as a stepmother if the biological mother has either died or completely abandoned the child. I think. To put it another way: a stepmother is someone who actually raises the child.
Stepmother is a legal term, clearly defined. In 60 years I’ve never heard it dragooned into any other use.
It’s much less common today but it was once the automatic norm to call an adult with no legal status but some kind of socially recognised special relationship to a family with children Uncle Hisname or, as here, Aunt Hername.