Does first strike damage resolve before regular damage in the same combat step or are they separate steps?

First strike and regular damage do NOT resolve in the same combat damage step — they occur in two distinct, sequential combat damage steps. This is governed by CR 310.1–310.6. If any attacking or blocking creature has first strike or double strike, the game conducts a first combat damage step exclusively for those creatures. Then, if any creatures with regular damage-dealing ability (or double strikers dealing again) remain, a second combat damage step occurs.

During the first combat damage step (CR 510.1), only creatures with first strike or double strike assign and deal their damage. After damage resolves, state-based actions are checked (CR 704.5g), so creatures that are lethal-damaged at this point die before the second step begins. Players also get priority and may cast instants or activate abilities between the two steps.

The second combat damage step (CR 510.5) then occurs for all surviving creatures that deal regular damage — including double strikers who deal damage a second time. Creatures that survived the first step but have since died from first strike damage simply don't participate.

Concrete example: Your 2/2 with first strike blocks your opponent's 4/4 with no special abilities. In the first combat damage step, your 2/2 deals 2 damage to the 4/4. State-based actions are checked — the 4/4 is not dead (needs 4 damage). Then in the second step, the 4/4 deals 4 damage to your 2/2, killing it. Both creatures survive the first step, but your 2/2 dies in the second. Had your creature been a 4/2 with first strike, the 4/4 would die after step one and never deal its damage back.

Key rules: CR 510.1 (first combat damage step), CR 510.4 (check for creatures with first/double strike to determine if a second step is needed), CR 510.5 (second combat damage step), and CR 702.7b (double strike definition).