A critter, to railfans, is a small locomotive, which can be either narrow or standard gauge, but more importantly must be quite tiny indeed. A critter would never pull something that could properly be called a train; a few cars, no more than half a dozen, would probably be its limit. A critter would rarely be hauling anything from place to place; the critter's domain was and is generally in one place, a rail yard or industrial plant, pottering around moving cars from building to building or making up and breaking down trains that arrive and depart under the control of larger power.
Critters are switchers in US parlance, or shunters in British, but there are switchers that are not critters. Switchers can, after all, be quite large; there were and are switcher designs that are larger than smaller road locomotives. It would be rare to call a locomotive of over 100 tons a critter, and generally they're a lot smaller.
Few of these locomotives were ever owned by real railroads -- the vast majority belonged (and in much smaller numbers still do) to industrial operations. Railroads might sometimes own one or two for use in very confined spaces, dockside lines or street railroads in industrial areas.
As originally conceived, the word was applied only to internal combustion engined industrial switchers -- gasoline or diesel powered -- but many would also count similarly diminutive electric or steam locomotives.