The Game Boy Advance SP does not have a built-in rechargeable battery. It uses a replaceable lithium-ion cell (model AGB-003, 3.7V, 600 mAh).
Third-party packs (e.g., Nyko, Intec) replace the battery cover and add a charging port + internal Li-ion cell. These let you charge via AC/USB but add bulk. Quality varies—read reviews.