In the sentence "He watched the girl run away," what's happening, grammatically? (See details please).

My grasp of formal grammar terms is shaky, but I’m trying to learn a bit more.

At the moment, the back half of sentences constructed like this are confusing me. (To be clear, I’m not confused about how to construct these sorts of sentences—I’m confused about how to describe what’s happening… I’m a native English speaker, and while I know these examples “sounds right,” I can’t explain why).

- He watched the girl run away.
– She saw the dog sniff the fire hydrant.
– Ella made her sister return the book that she’d stolen from the neighbor.

1. What would you call the italicized phrase (or clause)? (Or, if this type of pattern has more to do with the main verb than the portion I italicized, what would you call this type of sentence?)

2. How do you describe what’s happening with the italicized verb? I know that I’m doing something with the verb, but I don’t understand what it is. It’s not a main verb, it doesn’t seem to really have a sense of time (tense), but it’s also not an “infinitive,” (and it’s clearly not a “participle,” or “gerund,” and after that I’m out of terms I know)... so what is it?

Much thanks for any help! :)