I think there are 2 different terms for these tools.
Belt Sander - is found in wood working shops
Belt Grinder - is found in metal working shops.
That said I think there is a lot of overlap in what the owners do with theirs. Generally belt sanders are wider, 6" and up to really wide whereas belt grinders tend to be 1" and 2".
I've owned several smaller 42" x 1" and 42" x 2" metal grinders but also use them for wood at times and man, do they eat wood. Trouble is the wood dust builds up inside and when you grind metal afterwards the sparks ignite the wood dust and it smoulders until you deal with it.