I believe that what you are calling 'polynominal' might be more widely known as 'multinomial', that is, a nominal variable with lots of categories as seen in a multinomial logistic regression.

The distinction then makes sense: your standard logistic regression is modelling the probability of seeing the two values of a binary variable at different values of a continuous variable, while the multinomial logistic regression generalises this to a nominal variable with multiple values.

The reason a search engine would get confused (I ended up going via a dictionary) is that as you may or may not know polynomial without the N is a word for a sort of equation (and indeed, one that makes sense to see in a statistical context).

I could be wrong, but I do not think this term 'polynomiNal' is a common one, and in my own work as an industrial data scientist I tend to call your 'binominal' variables 'binary', and 'polynominal' simply 'nominal'.

There is always the possibility that I missed something.