What is the difference between a grip and a key grip?

There are several different types of "grips", each with varying levels of responsibility.

The Key Grip is basically the unit head, and reports to the Director of Photography on a feature. They are responsible for scouting the locations, ordering, arranging transport and setup of equipment for filming and lighting. They are sometimes billed as first company grip.

Other grips work with the lighting, cameras, camera cranes, dollies, setting up rigging for lighting, and other tasks relating to the filming and lighting. According to union rules, however, they do not touch lights or electrical distribution elements, that is the responsibility of the electricians onsite, who work under a gaffer.

There are a few different theories on where the term "grip" comes from, but it has been in use dating back to the early days of the circus. (Late 1700's - early 1800's).

So if you pick something up once, you're considered a grip?

-Mike Nelson, riffing their own credits in Mystery Science Theater 3000: The Movie (1996)

Indeed, A Key Grip usually doesn't do any gripping, that is to say it's just a fancy way of saying "Grip Manager". And while we're at it, Mike is basically right that Grips just hold things such as cameras and lights to make shots quicker to set up.