Do you need mods installed to play on a modded server?

I might buy a Minecraft server from a site called Beastnode. I can't create a server for some reason, so after a year of trying, I know I'll have to buy one. I was going to get one from Beastnode which allows me to put mods on my server. If I do, will everyone else need to have those mods installed also? The mods with all be mods for FML (forge mod loader). So, will they just have to have FML installed? Thanks in advance to anyone who answers. But only answer the questions I asked. I don't need to know how to make a Bukkit server instead or any of that. Just answer my questions please.

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Yes in order to connect to a modded server you will need the same mods on your client version. I highly recommend using modpacks from mod launchers such as ATlauncher and the Technic Launcher, it installs all the mods for you so you don't have to mess around installing them separately.