I have noticed there are two types of cutters for sheet metal. One a
nibbler, one a shear.

The one nibbler I see apparently cuts out small pieces, almost circles, and
imagine that would be for very fine work. The other "nibbler" has two
blades that are about 3/4" long that go up and down, pinching and shearing
the metal.

The third is a shear, much like a pair of electrified scissors.

A brief description of each and its use would be appreciated. When it comes
down to it, I will probably need all three for various stuff.

And lastly, I see some run on air. If one has a good compressor, is there
any important differences between the electric and air models?

This is going to run a few bucks, so wanted to ask first.

And is buying refurbished worth the savings or not? Problems later vs: new?

Steve