If a creature with first strike kills a blocker, does the surviving first strike creature still deal damage in the regular combat damage step?

Combat damage is dealt in up to two separate steps when first strike (or double strike) is involved. The first combat damage step (CR 510.1) handles damage from creatures with first strike or double strike. The second, regular combat damage step (CR 510.2) then occurs — but only creatures that did not already deal damage in the first step participate. A normal first strike creature has already dealt its damage, so it sits out the second step entirely.

CR 510.2 states explicitly: 'Each creature assigns combat damage it would deal to the defending player, a planeswalker the defending player controls, or a battle the defending player controls. If a creature was put into the first combat damage step and has already been removed from combat or dealt damage, it does not deal damage in the second step.' More precisely, only creatures without first strike (and without double strike) assign damage in the regular step — first strike creatures are excluded unless they also have double strike.

The key exception is double strike (CR 702.4b): a creature with double strike deals damage in both steps — first alongside first strikers, and then again in the regular step alongside normal creatures.

Concrete example: Your 2/2 with first strike blocks an opponent's 3/3 with no special abilities. In the first combat damage step, your 2/2 deals 2 damage to the 3/3. The 3/3 dies (assuming no regeneration). In the regular combat damage step, your 2/2 does not deal damage again — it already had its turn. The 3/3 never gets to deal its 3 damage because it was destroyed before the regular step.

So a plain first strike creature only ever deals damage once per combat — in the first strike damage step — regardless of whether its blocker or attackers survived.