Moderator:

Moderators are the starting point for staff members, they handle situations within the game and can handle reports on users on the forums, although they're limited they're given enough power to be able to do their staff-duties.

Admin:

Admins are the upper stage for a moderator looking to become more serious about their role, they're given a few new abilities like being able to handle unban appeals, being able to ban, spectate and noclip with a few others, you're also able to re-apply for this role if you have been admin in the past however, you need to get permission from a HA+

I've probably missed some points out but that's just the base-line of what they do.

Also note you have to be Moderator to apply for Admin, or like I said previously you have to had been Admin in the past to re-apply for that position.