Does a creature dealt damage equal to its toughness die immediately or during the next state-based action check?

Damage does not cause a creature to die the instant it is dealt. Instead, the game marks the damage on the creature, and then state-based actions (SBAs) are checked at the next opportunity — specifically, before any player would receive priority (CR 704.3). At that point, if a creature has damage marked on it equal to or greater than its toughness, it is destroyed as an SBA (CR 704.5g).

This timing distinction matters greatly in practice. Spells and abilities on the stack fully resolve before SBAs are checked. Multiple events during a single spell or ability resolution — such as dealing damage to several creatures — are all evaluated together when SBAs are finally checked.

Damage is "lethal" when it meets or exceeds the creature's toughness, but deathtouch also makes any nonzero damage lethal (CR 702.2b, 704.5g). In either case, the creature is not removed from the battlefield until the SBA check occurs.

Concrete example: A 2/2 creature blocks a 3/3. When combat damage is assigned and dealt simultaneously, the 2/2 has 3 damage marked on it (≥ its toughness of 2). Before any player receives priority after the damage step, SBAs are checked and the 2/2 is destroyed at that point — not mid-combat-damage assignment.

Because the creature survives until the SBA check, effects that trigger on damage being dealt (like lifelink or certain triggered abilities) will still function off that damage even though the creature will soon be destroyed.