Some notes on these 2 words if used in 'drinking alcohol' meaning,

Выпить can often be used in alcohol related context (used as a single verb). Examples: он вчера выпил (he drank yesterday), он выпил и ему нельзя садиться за руль (he has drunk alcohol and mustn't be driving), он сильно выпил (he drank a lot of alcohol), etc. - here it implies the fact of drinking, or instance(s) of it.

At the same time пить can also be used in this sense and it can sometimes mean a medical condition or a longer process. Examples: он пьет (he is a chronic drinker), он пил всю неделю (he was drinking the whole week), cf. он выпивает - means 'he drinks alcohol occasionally'

In neutral contexts (no acohol is implied) it seems that they work as usual verbs: пить is imperfect, выпить suggests the perfect tense (has/have drunk), they don't look different from regular verbs here.