The main connection types you will see are:
KR808D-1 - same thread as a 901 so they often fit the same devices, but for air flow the 901 has a hole in the side and the KR doesn't so it requires a slot in the battery post for air flow through the bottom of the cartomizer. The big advantages with cartomizers is that they are clean (they don't leak anything like regular atties) so you can pocket them without worry, and you don't have to drip them every five seconds to keep them going.
510 - Has a "male" thread on the bottom of the atty or carto instead of a "female" thread like all the others. Common in both cartomizers and regular atties. V4L cartos are KRs though. The biggest advantages of "regular" atties is you can change flavors frequently and with ease, and they usually last longer than a cartomizer. But they are messy.
901 - regular style metal atties that will work on all KR devices. People say it has better flavor than the more popular 510. Its also more messy IMO, leaking juice out the little air hole on the side.
801 - just a really big atomizer. I don't get the attraction. Female thread, no air hole, really big, no point.
Now you know your atties, not all of them, but at least the main ones. With my personal bias to cloud your judgement.
BTW you can buy adapters to use just about any atty on any battery so you can satisfy your curiosity without needing four different devices.