No, the 'admins' are people who work for reddit. 'Mods' are people who volunteer to work for reddit (the 'despots'). By the way, you should try modding a moderately large sub and see what you have to deal with. It is always easy to criticize until you are one having to do the work.
Unless it's changed completely since I bolted from there a couple years ago, they absolutely do. Anyone who had been using the site for more than a few weeks generally understood the difference.
That sites been eternal Septembered multiple times, to the point it's almost entirely unrecognisable. Reddiquitte isn't even a thing anymore, they now have "policies" and "codes of conduct".
I wouldn't be shocked if the meta has changed to call anyone with powers "admins" now.