According to Ecyclopedia Britannica anything 2000ft high (610 m) and over constitues a mountain. I really can't find any exact definitions of a hill except that it's smaller than a moutain. I can't imagine a hill being 1900 ft high. That's a pretty darn big hill if you ask me. A mountain is supposed to have steep and rocky sides. If you look at scientific descriptions of a mountain, they will tell you that its history goes back to tectonic forces - earthquakes, volcanos, etc. Some say a mountain is marked by having a peak ( it's called a topographic marker) while a hill doesn't have one.
In any case, those discriptions seem to be somewhat vague but the rule of thumb is excatly what you have just noticed - mountains are way bigger than hills.