PVP/PVE WOW servers?

When a server is marked as PVP (or PVE), does that mean it only offers PVP (or PVE) content and the other type; PVE (or PVP) is not present in the server?

In other words, should I look for a PVE+PVP server if I enjoy both dungeons/raids and PVP game-play? Or is this distinction only related to open world PVP?

I used to play on Sargeras years ago and would like a similar experience of leveling and questing (but gaining quick xp) while also being able to play endgame content, both PVE and PVP. Preferably on a highly populated server. Not sure how realistic this is, but it can’t hurt to ask around.