Yes, they are "loosely direct" sequels. Its hard to describe. Its all on the same time line, but the focus of the story is different each time. For every game the villains are different and have no connections with the previous one, also the characters you can choose from to play are different. The player characters of the last game become major story NPCs of the next game. You'd be lost on some of the lore, but you could still easily enjoy the story and the game. Since the characters you choose from are new to the borderlands world, the game treats your character as someone that doesn't know anything. So all the characters get their own introductions to you and things are explained to you as if you've never played a previous game before. This game also presents a ton of new characters to the universe like the owners of all the weapon brands. Borderlands shines more on its comedy, satire, and not taking it self too seriously. This is also the first game that leaves the home planet and you visit multiple worlds.
Best side mission ever.