A prematurely extinguished cigarette. This term is common among non-working teenagers who aren't actually old enough to smoke, who put out a cigarette half way through and save it for later.
I needed a cigarette SO bad and then I remembered I had a shorty in a zip-loc under my bed, so I went around back of the house and smoked it.
"Shorty" stems from the term "short list" (of guests to invite), and is a term of endearment for someone who is at the top of your list.
You're my shorty, you have to come to my party.
Dude, that shorty hooked up with 3 guys at that frat last night!
A regular ciggarrette ..not a 100
Afta i blazed i was feenin for a bogie and every1 only had shorties and i only smoke 100s so i robbed some white boys for money to buy a pack.