If an equipment is attached to a creature that becomes a different player's creature, does the equipment move with it?

Equipment that is attached to a creature remains attached when that creature changes controllers — the equipment does not automatically move to the new controller's side or fall off simply because of the control change. This is stated in CR 301.5d: if a permanent is attached to an object that changes zones or controllers, it remains attached unless a rule or effect causes it to become unattached.

However, there is an important caveat from CR 301.5c: if at any point the equipment is attached to a permanent it cannot legally be attached to — most relevantly, equipment can only be attached to creatures controlled by the equipment's controller — the equipment becomes unattached. So if the creature swaps to another player but the equipment is still controlled by the original player, the equipment will immediately fall off because you can only equip creatures you control (CR 702.6e).

The equipment itself does NOT move to the new controller of the creature. Equipment is a permanent independent of the creature it's on. It stays on the battlefield under its original owner/controller. The only question is whether it remains attached.

Concrete example: Your opponent steals your 2/2 creature with Triton Tactics, but your Sword of Fire and Ice is attached to it. When the creature becomes your opponent's, the Sword immediately becomes unattached and falls to the battlefield (still under your control), because you cannot have your equipment attached to your opponent's creature.

If somehow the equipment's controller also changed to match (e.g., through a complex effect that transfers both), the attachment could legally persist, since it would then be attached to a creature controlled by the equipment's controller.