For those that have never seen a pirate attack and your imaginations are running wild it's like this. There are no cutscenes, but another exact replica of the ship comes up and pulls right next to your ship with three cloaked smn type humes standing on the edge. No sky turning dark, no hell washing over the deck or anything. Everything is the exact same except now another ship is right next to you.
Anyway, they do their summon motion and a few crossbones appear on deck, maybe three. When you kill one off, they summon pose again and another one appears. If there's a smn hume on the other deck that's wearing what looks like a Vermillion Cloak, Blackbeard or Silverhook will appear, again with no cutscene.
They'll stay on for a while, then they despawn in a little warp-like vortex. The smn turn around and the ship pulls away.
Also, the music changes during the whole ordeal. Not quite as intense as BCNM music or empty boss, but it let's you know there's badguys on board.