The interconnected lock is usually a combination of one cylindrical lock and one tubular lock operated via a single motion.  The single motion is turning a knob or lever handle. 

From the locksmith dictionary;

n.  a lockset whose trim provides a means of simultaneous

 retraction of two or more bolts which may also be

operated independently

Many brands of this type of lock can be found but just as commonly you will find that an exact replacement isn’t available because most manufacturers haven’t made one for more than 10 years at a time.  It will typically be possible to find a new replacement but it will be a different brand and may even have a different keyway that isn’t compatible with any other locks you may have.

The trim plate on the inside has a mechanism that makes it possible for the single handle to operate both locks simultaneously.  The primary purpose of these locks is to meet a local fire code that prohibits a locking scheme that makes the user perform more than a single motion to gain exit.

If you have the loose hinge or building settling problems, you will now have two strikes to adjust for a solution.  If there is a problem with the inside trim that doesn’t allow retraction of both bolts any longer, you should call a professional locksmith for repairs.