Is it one queen bee per hive or per colony?
Every beehive contains one colony, and every colony has one queen. (Of course there are exceptions, like if a queen dies or is about to be replaced, but I don't think that's what you're asking.)

A swarm is a specific thing, when the queen and part of a colony has taken off from the original colony to form a new one.

I think Wikipedia works well if you need more information on beekeeping terminology:
https://en.wikipedia.org/wiki/Beehive

https://en.wikipedia.org/wiki/Swarming_(honey_bee)

Edit: To clarify, I only have experience of keeping European honey bees (Apis mellifera).