A for real hard hat is more than just a hard polyethylene shell. Inside each one you'll find a system for securing the hard hat to your head. There are two basic ways this is done:
Pin-lock suspension is basically like a man's belt that attaches to the users head with a locking mechanism. If you want to adjust your hard hat, you have to take it off and remove the suspension.
Ratchet suspension features a quick ratchet adjusting knob. If you want to loosen or tighten the hard hat "on the go" you simply turn the knob.
The typical hard hat will have either four point suspension/six point suspension. This is the actual number of clips that mounts the cradle suspension to the shell of the hard hat.
Manufacturers such as MSA and others offer "V-guard" protection, a large embossed V designed into the hat for added protection. And that is probably all you will ever want to know about hard hat suspension systems.