Moderator is essentially an admin. The original name was Basic Admin, but they persuaded me to change it to Moderator. They basically have every permission that admins do, except the ability to delete props/move other people's props or some other commands that I can't think of off the top of my head.
Admin is generally the highest rank that you can likely achieve. They generally make the final decisions in-game on the server. They are also generally the highest authority in-game.
Head Admins are essentially Admin "Overseers". They are in charge of keeping the lower staff in line and on their toes. They are responsible for the behavior and actions of all staff members online. They also deal with demotions/promotions/etc. They also usually have the final say in any in-game disputes/issues, only when called upon.
Super Admins are the cliché rank on any gmod server for basically the highest rank possible, with every single permission/ability. They can basically do anything that gmod makes possible. Usually on servers the Super Admin rank represents the "Owner" rank. Other servers make an "Owner" rank. Also, Super Admins (Or at least 1) are the ones who literally control the server. They code/configure/install/edit/anything to do with addons/server-side control.
Those are the basic definitions, except for Operator. In reality there isn't really much of a difference between all of them, more of a hierarchy. Hope this clears things up, I can go into more detail if you want.