I could be wrong, but I think Sting used the Scorpion Death Lock before Bret Hart used The Sharpshooter.
The similarity in the names of Sting's finishers can be simplified down to his gimmick. It is continuity in his character down to his moves.
The Stinger Splash is a great move. Especially when he delivered it in his early days. He would launch into the air and crush his opponent in the corner. It usually came off pretty great. It watered down over the years, like most moves do.
The Scorpion Death Drop was/is an awesome move. During his days when he was opposing the NWO, it was perfect move for him to use and apply quickly. It had plenty of impact and came off looking awesome. He would usually come from behind the guy, so he was always in the right angle to hit it. It didn't take much for him to apply it, so he could hit numerous members of The NWO with it, in a short amount of time.
Also, when a move is used for X amount of years, it could get watered down. After all the years go by, other people start to use it, as a move separate from being a finisher. Then when the guy that used it as his finisher uses it, it isn't something only HE does anymore. But, it also could be considered Sting is the MASTER of said moves is why he finishes his matches with them still.
I think it is fine in certain cases if more than one guy uses a particular move as their finisher. Especially when they are in different companies, they both do the move so well, and they are 2 top guys, such as Bret Hart and Sting. They both had used the move to win World Titles and many other matches. So, when they ended up in WCW together, there truly was no point in having either switch. Having them battle to see who uses it better is a better angle then most ways to go with it, and it adds another angle to a feud that wouldn't have been there if they didn't use a similar move.