Admins are employees. The people running the subs are mods. There aren't even 1% of enough admins to moderate the subreddits, but there are enough to police the moderation stances of the large subs.

Admins are employees, sub owners are unpaid volunteers.

Reddit admins are Reddit employees.

Reddit moderators are (generally) not Reddit employees.

Regular users create the subreddits, but they all belong to Reddit.

I'm pretty sure the admins have installed mods before on subreddits where they didn't like the mod team. I think I remember people talking about it at one point, but I can't remember specifics, so I'm not entirely sure. (They do it for abandoned subs all the time, but that's different.)

I know over a decade ago when the IAmA subreddit creator was going to shut that subreddit down one of the admins said they'd take the subreddit over and put new mods in if he didn't change his mind. But at the time the admins weren't throwing their weight around like they would eventually, so it wasn't a consensus thing, just one admin talking.