It could be that Calza, with the feminine ending, refers to (or used to refer to) a longer, stocking-like, woman's sock, while Calzino - masculine - refers to a shorter man's stock. Maybe over time they changed from having the stricter gender-based meanings to having broader definitions. Just a bit of idle speculation.
In the section marked clothing, duo asked for "the socks" When I entered i calzini, it was marked wrong, and le calze was considered the correct answer. That would be correct if we were referring to the stockings, but to be clear, duo asked for the socks, and the plural of that is calzini. This needs to be clarified.
Why does Duolingo say "Mark ALL correct meanings" while its never more than one correct answer? I have never seen a multiple choice thing that had more than one correct answer and if you mark a correct answer AND a somehow incorrect answer the whole answer counted as incorrect.