Besides all of the base versions, there are special versions of every weapon in the game, coming as Enlisted, Professional, or Elite (in increasing order of rarity). You can earn Supply Drop weaponry from completing challenges, or most often, simply by participating in Multiplayer matches. Clan Wars and special promotions are another potential source of drops.
Supply Drop weapons aren’t necessarily any better than the base version. They usually trade off one stat for another, but they sometimes have unique attachment quirks. All of them have cool paint jobs, and many have custom models. Strut your stuff on the battlefield.