A music label deals mostly with producing and promoting bands and artists careers. they’ll sell different products like merch, CDs/LPs, and promote shows and live performances. Also, they normally have major control over the registering of artists master recordings.

Publishers manage the copyrights of songwriters and/or labels that are associated with them and promotes these people's work by offering their catalog as a product. They often negotiate these works with labels that are looking for songs to synch. Publishers will have partnerships with different music societies from all around the world to ensure that every play from their catalog gets credits as it should.

Music Societies are responsible for generating and registering different creator identifiers, reporting to creators and publishers on their share of the revenues. You can have different types of Music Societies, like CMOs, which collect both performance and mechanical rights, or more focused companies like PROs (performance) or MROs (mechanical). Music societies will work with publishers and labels, reporting to them all relevant information about the revenue of every creator and getting their information to a worldwide database.

Labels work more with a performers career and master recording creation, publishers work with intellectual property management of their clients, and societies work generating and managing creator identifiers, also they work on oversight of all data related to music consumption.

You get both. Every time you reproduce a song through a DSP, they’ll pay performance rights because you’re reproducing a song/recording, and also pay mechanical rights because you have a cache data of that song stored in your device. Whenever you download or buy digital music content you receive both too, because you’re storing data and also having access to a preview of that song.