No, there is no untethered jailbreak yet. Jailbreakme only supports up to 4.3.3/4.2.8, it will not work on any firmware newer than that. Secondly, once the iOS5 untethered jailbreak is released, you will need to jailbreak from your computer.
It's redsn0w that has the Tethered Jailbreak right now. I think it's safe to say when a fully Untethered is released... it'll be through redsn0w as well.
Your question doesn't make sense. Greenpois0n and limera1n are computer applications, they cannot be jailbroken. Since the Chronic-dev team(the people behind greenpois0n) are working on an untethered jailbreak they might still call it greenpois0n or they might change the name completely, nobody knows.
The things is, watevur34, it doesn't matter what the name of the "Jailbreak" application is. Wither it's called "limera1n" or "purplesn0w." For the most part a Jailbreak is a Jailbreak. So far... the team working on "redsn0w" has got things going the farthest. Look for it to be the first "Untethered Jailbreak" available.
Purplesn0w is an old unlock tool that was developed by GeoHot in 2009, he was just saying it doesn't matter what they name it, they all have the same end result.