Pirates used all kinds of weapons.
Whatever they could get their hands on; stolen or otherwise.
Weapons varied somewhat as the ages rolled by and eventually guns were invented. Pirates used knives, dirks, swords, bows and arrows, spears, axes... maybe a severed arm... What a disarming thought, eh?
Oh, don't forget, clubs and mauls...
Maybe a scary face or a beard with lit fuses, as in a method used by the famous pirate, Blackbeard.
The blunderbuss, cutlass and the pistol are the pirate weapons most people are familiar with. A pirate could just as well have wielded a gladius; the short thrusting sword of the Romans. Perhaps a Katana from Japan might have been the weapon of choice since they are very effective for removing obstacles such as someone's head. The knightly long sword would have been somewhat unwieldy on board a sailing vessel albeit such a sword is very effective for taking off an arm or cleaving a man in twain. Boarding axes were very effective weapons and were the model for modern day firemen's axes. In the etchings of pirates wielding weapons, note the chap wielding a halberd. That weapon was first developed by the Swiss. An early Swiss Army Tool which was highly effective at dismembering and disembowling, decapitation and otherwise fucking up an opponent. Piracy was and is still to this day, a Bloody Business.