Stop your server before enabling or disabling mod profiles.
In the Game Management console, select Mod Manager from the main page. Mod Manager will offer to install any of several popular mod configurations for you. You should only have one mod profile active at a time. Click “install” to enable the mod profile of your choice.
Minecraft has two seperate mod platforms: Bukkit/Spiggot and Forge.
Bukkit/Spiggot is an extended version of a regular Minecraft server that also supports sever plugins which can alter the game. Players connecting to the server do not need to install any mods on their client.
Forge (Tekkit/FTB) is a mod API for both client and server which forms the base of many popular mods. Players connecting to the server must have a modified Forge client and the corresponding mods. The player and server must have the same versions of Forge and all installed mods, except for some mods which run on only the client or only the server. (JourneyMap is an example of a popular mod that is client-only.)