The term draw in a larger sense means simply to move something by pulling on it.
One common sense of the phrase came from pulling on the reins of a horse or team of horses to cause them to stop. Now, "draw up" has expanded to mean bringing any vehicle to a stop.
From its original meaning, also, "draw up" can also convey the sense of pulling something more tightly together, as in "draw up close to me" or "draw up a chair."
The first two sentences you gave are examples of the first meaning, simply to bring a vehicle to a stop ("the train stopped at the station" and "he stopped his car outside my house").
Your third sentence actually invokes the second meaning, evoking the idea that the train was pulled in close to the station (although, in this case, it did also happen to be a vehicle that came to a halt).
Note that it's not even required to come to a stop to "draw up" to something. For example, "I was driving on the highway and a large truck drew up alongside me."