Think of the FC's as a large scale global company. You can still belong to multiple LS's, but only one FC.
So the LS's would be your little guilds or union (even if the members of the LS's aren't in the same FC). LS's have no in game bonus, but tend to be purpose specific. You might have a gathering LS or a crafting one, you might have one for Coil runs or other end game content... but you always belong to your larger FC and whatever benefit they choose to boost you get (bonus XP, cheaper teleports, reduced gear wear, longer food time, or whatever).
Your FC is one that should mean something to you, a long term investment with a diverse group of friends. The LS's would be for very specific things, either information or focused content with zero bonuses other than that availability of people with a focused interest.