In other words 1 LS can only create 1 FC. A player can only join 1 FC. The benefits of FC worth noting is status buffs.
Linkshells are chat channels and are meant to link people together to make it easier to find groups and/or socialize. FCs are the "guilds" of this game and will gain new functionalities and features over time. You're likely just used to linkshells being the "guild" system from XI or 1.0.