Yes, updates, plural. The level/cap update has two parts.
- The free update increases Eridium capacity to 500, and adds more ammo, backpack, and bank upgrades to the black market. There's also "Ultimate Vault Hunter Mode", which is the third playthrough, which greatly increases difficulty, skips the starter tutorial missions, and can have it's progress individually reset from the menu (opposed to starting a new character for further plays).
- The paid update is $5/400MSP (free for pass owners as pokefloot says below), and that's what adds the raised level cap (up to 61, complete with 11 more skill points), and a new class of "Ancient" e-tech weapons.