I think that in the past zipper was the noun and zip the verb, usually as the phrasal verb zip up. If zip was used as a noun it was slang for speed or energy. But more recently I've observed zip being used as a noun referring to the fastener. If I didn't want to use zipper for some reason I'd go with zip fastener rather than just zip to avoid ambiguity.
Of course, in the USA only zip is also short for zip code, their numerical postal code.