As easyeight says, Carrier Command is a supplement to Fighter Command. Fighter Command is a stand-alone ruleset. (Good one, IMO!) But you have to have Fighter Command to understand how to use Carrier Command. Carrier Command adds carrier ops to Fighter Command.
It might be possible to use a different set of space fighter combat rules and "marry" them to Carrier Command to add the carrier ops. But it would be a shotgun wedding.
There's also a supplement called "Carrier Command" which is focused on being a Carrier captain and managing your space assets to complete a campaign. It has expanded rules for electronic warfare, boarding, etc.
Do the two titles complement each other or completely separate?
Fighter Command is the ruleset and Carrier Command a supplement and it needs the ruleset to play it.