As far as terms "belt grinder" and "belt sander" they are both fairly interchangeable. They both use belts and they both sand/grind material away.
That being said, when I hear "belt grinder" I usually think of a specific array of "sanders" used for removing and shaping metal. Belt sander usually makes me think of wood sanding machines, though belts can usually be purchased for either metal, wood, or whatever other material you want to work with on each "type" of machine.
The biggest thing you should be concerned about is really 3 things:
belt size
power
configuration
Belt size: you want a machine that's going to be practical for making knives. Now don't get me wrong. Plenty of guys have used plenty of different belt sizes to grind knives on, from 1/2" wide to probably 30" wide or more. I'm not saying it can't be done on one size or the other. The majority of experienced knife makers will tell you, however, that a 2" wide belt is one of the more ideal widths, and 72" long belts are the ideal length. Why? Well, for one, there isn't a grit, type, weight, material, etc... that you can't find in a 2x72 configuration. Not necessarily so with a 2x48 (though there's plenty to get results you want) 2x42, 6x48, etc....
Also, you have a little more control with a 2" wide belt IMO, than say, a 4" or 6".
Power:
Appropriate power will depend on belt size and configuratoin (see below), but typically, you want too much power more than "not enough".
For two wheel grinders (drive wheel + contact/idler wheel) I'd say 1 HP is a MINUMUM, especially if it's not direct drive (which most are).
If it's a 3 or 4 wheel (drive, idler AND contact/2 wheel platen) then you probably want AT LEAST 1.5HP with 2 being even better. If it's a belt/pulley drive configuration, you'll lose even more power when blade touches belt.
Configuration:
This depends on what kind of grinds you want, and what kind of machine you have. Some machines can 2 wheel machines can hollow grind AND flat grind, some are really only good for one OR the other. A machine like a KMG or NWGS will typically have 3 to 4 wheels uses tool arms for doing either/or.
As for which one is better, I'd say you get a little better control and tracking with a 3 wheel, but that only goes as far as how well the machine is set up and aligned.
Personally, I prefer a 3 to 4 wheel grinder with exchangeable tool arms for versatility. That being said, if a 1/3hp 1x30 Harbor Freight belt sander is all you can afford, then by all means, it's better than nothing. But if you have $500 to $2500 to spend, there are some very nice options out there for the money.