"Short story" can be used as an umbrella term for a broad range of story lengths. It's important to understand both the terms and how the word count can affect the way a story reads. That way you can pick the type that suits your reading style.
I will be listing word counts as a way of indicating length. Most paperback books have about 250 words on a page. This can vary depending on how big the book is or what type of e-reading device you are using. But this will at least give you a rough approximation.
Novel - Will typically be over 40,000 words. We're not worried about these here on Short Story Symposium.
Novella - 17,500 to 40,000 words. These usually read like mini novels. The lower word count means that the plot tends to be more straightforward. There will be character development (hopefully) but don't expect tons of side characters and sub-plots.
Novelette - 7,500 to 17,500 words. Very similar to the novella in terms of how it reads. Depending on who you ask, some people squish the novelette and the novella into one category. There is a bit of a grey area around that 7,000 word mark where the story could read more like a short story rather than a mini-novel.
Short Story - 1,000 to 7,500 words. This is the actual short story rather than the umbrella term. Short stories are not intended to be read like a mini novel. The goal is to present an single idea (eating an ice cream cone) rather than an entire plot (my day buying an ice cream cone). A good short story will instantly pull you in with minimal description.
Flash Fiction - Less than 1,000 words. Sometimes referred to as literary poetry. Flash fiction must be even more precise than a short story. The goal is to use as few words as possible in order to let the reader finish the story in their mind. The best example is Earnest Hemingway's immortal six word story: "For sale: Baby shoes, never worn."