Based on experience with tons of these...for both keyboards and mice..
KEYBOARDS
1. The short connector is far more common for keyboard cables. It was generally used with the short keyboards (IIGS, Apple Keyboard, Apple Keyboard II).
2. I have seen the long connector used mostly with the extended keyboards. Most AEK IIs I've come across have it.
3. There are exceptions. I have an LC 550 with its original keyboard (one owner before me so I have proof), which was the short AK II. It has a long cable.
MICE
1. The only mice I have seen with long connectors are those which came with portables. I have exactly one, and it was included with a PowerBook 170 I picked up years ago (and no longer have). I kept the mouse since it is in immaculate condition and has the long connector. Just a guess, but maybe the mice purchased as accessories also had this? Its serial number indicated 1989 for a manufacture date, so it could have been at a dealer as a spare part and was purchased by a trackball-averse PowerBook customer.
2. Based on the mice I have seen with those connectors, all are the black ball model made in Taiwan. All US and Malaysia models I have encountered are the short connectors, as are most from Taiwan. (Did Ireland also make this style?)
3. The ADB Mouse II (round mouse) only seems to have the short connector.
4. The sticker was included on these mice but fell off easily. I've been using the same mouse for nearly 27 years on my LC. It fell off after about 6 years. That mouse was used heavily and was almost always on a pad. Chances are good your mouse without a sticker suffered the same fate as my LC's. It was a protective measure for the Teflon underneath.
Random question for Johnny, the OP--what kind of keyboard is that next to your mouse? It doesn't look like an original Apple one based on the font used on the keys. Curious as to what make it is.