Do both players get priority between each combat step or only between phases?

Priority is granted at the beginning of every step and phase, not just at phase boundaries. The combat phase is divided into five steps: beginning of combat, declare attackers, declare blockers, combat damage, and end of combat. Players receive priority at the start of each of these steps (CR 116.3).

Specifically, after the active player receives priority and all players pass in succession without taking any action, the current step ends and the game moves to the next one (CR 116.4). This means there is a full round of priority in every combat step, giving both players windows to cast instants or activate abilities between each step.

The declare attackers step, for example, works like this: the active player declares attackers (CR 508.1), triggered abilities go on the stack, then the active player receives priority (CR 508.6). Both players may respond before the game advances to the declare blockers step. The same applies to every other combat step.

Example: You attack with a 2/2. After blockers are declared, your opponent gets priority in the declare blockers step and casts Giant Growth on their blocker. You then get priority and can respond with Shock to kill the blocker before the spell resolves — all still within the declare blockers step, before combat damage is assigned.

There is one nuance: if no spells or abilities are on the stack and both players pass in the declare blockers step, the game moves to the first combat damage step. So players always have a chance to act between steps, but the steps advance once everyone passes (CR 116.4, CR 509.3).