Are Forge and Bukkit compatible (Minecraft)?

I wanted to ask if you actually mods with Forge can actually mix with Bukkit plugins and if then each forge individually via the Internet must be able to join the server or if you only need to install Forge on the server but no one else installed it Must have in his own Minecraft

No Forge and Bukkit are not compatible.

But Sponge combines both. https://www.spongepowered.org/

So you can install plugins and Forge Mods on your server.

If you have game-modifying Forge Mods on the server, you must of course also have each client installed to join the server. Otherwise, the player gets a message that he misses the mods and he does not come to the server.

Client and server mods, on Forge, must be exactly the same version.