Recently I have seen the opinion that napkin is correct or posh, depending on your point of view and serviette is the opposite.
In my childhood it was a generational thing, my great aunt and grannie used napkins, or table napkins, my parents' generation spoke of serviettes. Feeling no doubt superior, as they were demonstrating a knowledge of French.
Babies wore nappies to my parents' generation, the older generation spoke either of nappies or napkins in that connection.
Napkin means a small piece of cloth,
Something similar seems to be happing with the word "dessert" which we are now told is incorrect, one should speak of "pudding" whether the dessert is a pudding or not! And " a sweet" instead of "pudding" is apparently quite beyond the pale. (Did I hear someone say "common"?)
Sorry if this really belongs in pendants' corner.