acabar vs terminar
Both mean 'finish' and are often interchangeable — but acabar also means 'just did' and 'run out of', and terminar is the cleaner choice for completing a task.
terminar
To finish or complete something — the neutral, task-oriented verb.
Terminé el informe a las cinco.
I finished the report at five.
Completing a task. Acabé would also work, but terminar is the safe default.
¿A qué hora termina la película?
What time does the film end?
Events ending. Both verbs work.
Terminaron la relación.
They ended the relationship.
Terminar can take a person as the one ending things: 'terminar con alguien' = to break up.
acabar
To finish, but also: acabar de = to have just done, acabar con = to put an end to, acabarse = to run out.
Acabo de llegar.
I've just arrived.
Acabar de + infinitive = just did. Terminar can't do this. Essential structure.
Se ha acabado el café.
We've run out of coffee.
Acabarse = to run out. 'Se me acabó la paciencia' = I ran out of patience.
Acabó pidiéndome perdón.
He ended up apologising to me.
Acabar + gerund = to end up doing. Great for stories.
Tricky bit
'Acabo de comer' (I just ate) is a present tense verb with a past meaning. Don't try 'terminé de comer' for the same sense — that means you've completed your meal, not that it just happened.