It’s even more complicated. There is the verb попи́ть, another perfective counterpart of the unprefixed пить.
Попи́ть means ‘drink some’ while вы́пить is ‘finish drinking’. Although, they are interchangeable in many cases.
Moreover, the verb вы́пить has its own prefixed imperfective form выпива́ть ‘drink (a certain amount)’.
E.g. «Я выпива́ю 5 ча́шек ко́фе в день» ‘I drink 5 cups of coffee a day’.
Another nuance is that the pair выпива́ть—вы́пить often means ‘drink alcohol’, especially without a direct object specified.
«Он ча́сто выпива́ет» ‘He drinks hard’
«Хо́чешь пить? — Нет, я хочу́ вы́пить» ‘Are you thirsty?’ ‘No, I wanna booze up’