Simple answer - there are POTENTIALLY 3 money streams from your musical work.
Mechanicals - ie: money generated (normally from a record company of some kind) from actual physical sales.
License Fees - a license is generated and paid for when a client/user wants to use your music and synchronize it to a video, Film, TV show, Web page, etc.
Performance Royalties - these are what I believe you are eluding to and in the USA are paid by BMI, ASCAP, SESAC - all PRO's - Performing Rights Organizations.
Also, in this brave new world sound exchange may be collecting performance royalties for you in places BMI / ASCAP can't reach....yet.
The copyright office does nothing more than register and (possibly in the case of a dispute) verify that you wrote the piece and registered it on such and such a date.