As my coach would say, stop over-thinking it. Just pick up the damn bar and put it down. Either or both are fine. The overhead squat is also excellent, but vastly more difficult.
Aside: the Olympic snatch is an amazing feat of strength, agility, form, athleticism, mechanics, balance, all of it. It's really a thing of beauty to see done well.
Just watch this - https://www.youtube.com/watch?v=cL1T-jKdTqo
Starting at 4 minutes. Pyrros Dimas is competing in the 85kg (187 lbs) category. He lifts 178 kg (392 lbs) over his head there. 392 lbs. Most people couldn't pick that bar up off the ground, much less get it over their head.