To use speedrunning terms, "beat" to me means "Any%" (i.e., beat the final boss, finish the story, get to the end credits, etc.), whereas "complete" means "100%" (i.e., clear every questline, obtain every item and milestone the game keeps track of, etc.).
In general, I beat games. The last game I completed was Mario Odyssey.
In general, I beat games. The last game I completed was Mario Odyssey.