Most is taken directly from their wiki's.
Minecraft Forge is a Minecraft API which allows almost maximum compatibility between other Forge mods. It contains a clean room rewrite
of RML (Risugami's Modloader) which allows compatibility with modloader mods. It contains hooks into the base Minecraft files that allows
modders to make their mods more advanced without editing base classes.
Bukkit is a Minecraft Server mod that completely changes how running and modifying a Minecraft
server is done - making managing and creating servers easier and providing more flexibility. Read More
The two, are in fact something completely different.
Bukkit & Forge are not compatible, they are not the same.
If you want to have forge compatible with bukkit, you will have to look
in to ForgeEssentials which is built for the specific reason to be compatible with Bukkit servers.
The more you know, the less of a fool you look like in a chatbox.