Cave Mountain, in the Mojave Desert, is a good example of an erosional mountain. The 300-meter rule is a convention; sometimes people limit mountains to 600 meters. Another criterion sometimes applied is that a mountain is something worthy of being given a name. I think it depends on the kind of country—in the Alps, for instance, quite a substantial peak may not be singled out for a name whereas in Kansas it very well might.
Volcanoes are also mountains, but they form by deposition.