As far as I can remember from my schooldays (best days of your life year right), the short part refers to the length of time that the story relates to - i.e. the story could be pages long but if it describes an event that occurred over say a couple of hours, then it could be described as a short story.
I think it's actually the other way round - 'short' refers to the length of the story itself (page/word count). Just so happens that its difficult to write about great swathes of time in a few pages, so a lot of them refer to small incidents. There's no hard and fast rule that determines when a short story becomes a novel - though I suppose that's why people keep referring to 'novellas'.
Many years ago I heard that a novel is defined as being more than 39,000 words - but I have never heard the same definition again since, so I presume it was one person's opinion rather than a definitive thingy.