I'm a SAMRO member, and I also have a joint membership arrangement with PRS in the UK. That probably says more about how I've learned to handle music royalties than an abstract definition would.
SAMRO administers performing rights for composers, songwriters and publishers. It licenses relevant public performances and communications of music, then distributes royalties under its rules and agreements. Radio and TV are obvious examples, but it's only one part of the rights picture. Registering a composition is not proof that a broadcaster played it, and a television appearance doesn't automatically turn into a payment next month.
What my own statements have shown me
I've had Blue Banger reported on The Ranakas and Our Perfect Wedding in my South African royalty statements. A later foreign statement also included Sky Sports Golf. Those are specific usages I can point to. If I only looked at the total paid, I'd miss the interesting part: which tracks were used, where, and in which accounting period.
Fountain of Youth is another example. Its use on CNN's Inside Africa generated most of what I've earned from that composition. One of my foreign statements separately showed CNN and SoundCloud activity for a particular distribution period. That's not the track's complete earnings history. Statements are snapshots, and it matters which snapshot you're reading.
Why PRS matters in my situation
I've been unhappy with aspects of how my international royalties have been collected through SAMRO. That's part of why I chose a joint SAMRO and PRS arrangement. I wanted greater visibility and a different collection route for relevant foreign activity. I'm not suggesting that SAMRO never collects internationally, or that two societies should both collect exactly the same right in the same territory. Membership mandates and territorial arrangements need to be understood properly.
My catalogue is spread across publishers, genres and territories. Some tracks have earned repeatedly; many haven't shown up on a statement yet. I keep an eye on cue sheets, composition titles, alternate versions, publishers and international usage because all of that can affect whether I can trace what happened. Being registered is only one step in that process.
The other organisations still matter
CAPASSO deals with mechanical rights for its represented repertoire. SAMPRA operates in the area of neighbouring rights in sound recordings and performances. These aren't simply other names for SAMRO, and signing up with one organisation doesn't automatically claim every right in a song or recording.
Before I tell another producer to register, I want to know who wrote the composition, who owns the master, whether they're signed to a publisher and where the music is likely to be used. Get the splits and titles right, keep the cue sheets where you can, and follow up when usage doesn't appear. That's the less glamorous part of sync, but it's where a lot of the long-term value gets protected.