Pirates are the heavy metal fans whose ships leak green goo. They have a crappy attitude, crappier ships, and suicidal bravery - they love to attack built up defenses.

Planetary militia are handfuls of TEC ships guarding the uncolonized planets in order to slow down expansion and give you an opportunity to level up your capital a bit. Some of them are Zapp Brannigan types dashing themselves against hopelessly superior firepower, but some of the Desert and Terran militias can be downright mean - more than a match for a lone capital.

Those are technically named pirates sometimes... But they are lone ships..

No pirates means no pirate FACTION... a pirate faction has a "pirate base" planet with massive defenses. it produces a massive armada every 15 minutes to attack the player with the highest bounty (you can place bounty on other players and vice versa). And collect said bounty by killing structures and ship of said player.
If nobody has a bounty they will randomly attack (but the AI will usually place a bounty on you to make sure the pirates attack you and not him).

I honestly don't like the current pirate implementation... other people didn't also, thats why in v1.02 a "no pirates" option was added.
Ways of modifying the way pirates work are currently discussed...