Bukkit was (I think) the first Minecraft server variant that supported the use of plugins, which added to the gameplay without the client needing to install anything besides Minecraft
Then Craftbukkit came along, which is a fork of Bukkit, and I guess it just has some implementations and features that people wanted, but Bukkit never implemented.
Spigot's nice because it supports both Bukkit and and Craftbukkit plugins, along with the ones made for it
PaperSpigot is a fork of Spigot that has some fixes and workarounds for implementations of non-normal features
It's buggy, though, so not many people use it. It's also hard to find
MCPC was a neat thing that let people have a hybrid Forge and Bukkit server
Cauldron came along and picked up from where MCPC left off
KCauldron is a variant of Cauldron (not sure of the difference)
Cauldron received some sort of DMCA complaint or something and stopped development after 1.7.10 :(
When that happened, a new project called Sponge popped up, which supported 1.8. It's still in beta, but I use it and it's not bad
Sponge has two variants: Vanilla and Forge
Vanilla is just competition against Spigot and such
Forge is closer to Cauldron
The problem with Sponge is that it needs its own special plugins (I guess to avoid the DMCA issues)
However, there is some sort of API/framework that lets you install Bukkit plugins to both Vanilla and Forge Sponge, but it's really hard to setup, as far as I've tried.
It is only Bukkit, but that's still something, if you can get it set up
This is what I know. It may not all be correct.