Shortbow +1 is a magical weapon. This appears in Baldur's Gate and all subsequent games. When this weapon is compared to a normal shortbow, it has a +1 bonus to damage and THAC0, has speed factor one point lower and with a weight of 2 lbs, it's one lbs lighter.
Shortbows were the first to be developed, although they were not called such. This is more of a default term that refers to anything which is not a longbow. Shortbow staves are about five feet long on the average. As the years passed, attempts were made to increase bow ranges. Bows were either given longer staves or flexibility was increased with no change to the length. The former resulted in what is now called the longbow.