Does first strike damage resolve before regular combat damage in the same combat step?

When one or more attacking or blocking creatures have first strike or double strike, the game adds an extra combat damage step before the normal one (CR 700.4). So combat damage is divided into two distinct steps, not two events within the same step.

In the first combat damage step, only creatures with first strike or double strike deal their damage (CR 702.2b). State-based actions are then checked — creatures that took lethal damage are destroyed. Priority is passed, players may cast spells and activate abilities, and only then does the game move on.

In the second (regular) combat damage step, creatures with double strike deal damage again, and creatures with neither first nor double strike deal their damage for the first time (CR 702.4b). If no creatures with first or double strike are in combat, the extra first step is skipped entirely and there is only one combat damage step.

Example: Your 2/2 first striker blocks your opponent's 3/3 vanilla creature. In the first damage step your 2/2 deals 2 damage to the 3/3. State-based actions see the 3/3 has not yet received lethal damage (it needs 3), so it survives to the regular damage step — but wait, it needs 3 and only received 2, so it lives and then deals 3 damage to your 2/2 in the regular step, killing it. First strike does not inherently kill larger creatures; it only means your creature's damage is dealt and checked before the opponent's.

The critical takeaway: first strike damage and regular combat damage happen in two separate steps with a full round of priority between them (CR 506.2). A creature that dies to first-strike damage in the first step never gets to deal damage in the second step.