Work profile is basically a second set of apps with a little briefcase badge that coexist next to your other apps. You/work chooses which apps are installed. They can't access the data in your actual profile and vice versa. You don't log out and in, it's just 2 containers spaces.

Private space is basically another such container, meant to be a 2nd personal one, but the apps aren't seen next to the others ... Theyre inert and hidden until you unlock the private space (pin/print/etc)

I think Android 15 is needed or thereabouts.

IDK about this 3rd party one being mentioned by adding it to my todo list