Sort of!
TV in the US is handled (more or less) the same as music copyright and performance royalties everywhere else, AFAIK: The producer/prodco pays the composer for a licence to copy the music into the program/film (the sync fee) and then the composer gets a performance royalty when/if the program airs. So that's a sync fee PLUS a performance royalty, two different payments for two different things, neither of which is payable by the distributor BTW. The only difference is with US theatrical presentations where, for whatever legal loophole, there is no performance royalty, only the sync fee.
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Sorry not seeing what you think I was "sort of" correct on by your response.
I can break down TV music more clearly for you, from personal experience even if you'd like. As a musician I got paid a service fee from the production company to write and record a theme song. This was lucky actually, usually musicians forgo this just to get attached to something, but I was full of myself at the time so I asked and strangely I received. So I got paid directly for the creative process and delivery of the finished broadcast ready product, nothing to do with licensing yet.
Now the production company doesn't pay me, the artist, to license something, because I don't know what to charge them or how to track it. However before I handed my finished song off to the production company I registered it with ASCAP as the publisher (me) and the writer (me)... 50/50. To my surprise the production company hit me back and said they wanted half the publishing. Remembering I already got a chunk of change up front and realizing it was a nice opportunity, I said sure and signed them on legally as co-publisher of just that one theme song. So now I'm at 25/50. Once that was all settled they paid ASCAP to include the song (that they paid me to write/record) in their show. A one time fee (el syncho de mayo) to be used on the show in perpetua. I have no idea what they paid to make that happen, but I'm thinking it wasn't to bad based on my pedigree and the shows budget. It may have even been free. I as the artist don't see any of that, that's how ASCAP makes theirs. Of interest is they rolled up the synch fee with the master fee because I was the owner/creator of the song
and the recording. That part gets way more complicated when its separately a writer's song, an artists performance and a labels recording.
[Music for Theatrical Released Films in the US work basically the same way up to this point]
Now it's the networks turn to pay. They take the show they purchased from the production company and its accompanying music cue sheets provided by the production company and submit them, along with the networks own records of the shows air dates and times, to ASCAP. ASCAP crosschecks all the factors and weights (length, placement, number of airings, is it incidental or a theme, etc) and charge the network a performance fee to use those songs. BTW when you go into a bar and hear your favorite song playing, from either the sound system or a cover band, that bar is paying performance fees for that music as well. ASCAP collects these monies, takes 10% and pays me the rest as my publishing and performance royalties quarterly, depending on if (and where and what time of day) the show is airing of course. And don't forget the production company is getting 25% when this happens too, if you recall my deal.
Back to Film for a second, even though an artist doesn't get these performance royalties (as in television) it's worth noting that if they end up on the films soundtrack, they will recoup all of the appropriate royalties based on album sales, digital downloads, radio play, etc. The marketing juggernaut that is theatrical film can propel a little song a long way and boost their royalties in all these other mediums much further than artists receiving standard royalties with hit songs on the radio.