Story Lengths
Small Forward
Depending on the length of the prose, one's story can fall under a variety of categories (short stories and novels are common ones). There is no end all ruling on how many words constitute a story as what--different groups have their own ideas of this--but here is a list of estimates.
List
Micro Fiction - About 100 words
Flash Fiction - Under 1,000 words
Short Story - 1,000-10,000 words
Novelette - 10,000-20,000 words
Novella - 20,000-50,000 words
Novel - 50,000-150,000 words
Stories of over 150,000 are usually divided into two novels.
End Notes
Not only are the numbers disputed, the names are too. Sometimes they are melded together; for example, some consider micro fiction to be short flash fiction and not a stand-alone type. Sometimes they are broken down further; some would add "sudden fiction" between flash fiction and short stories in the above list.
The rule of thumb is to check a specific publication's guidelines when submitting your piece.
Word Count Tool
Keep in mind that word counters are not 100% accurate.