JACAP is a collective management organisation which collects licence fees from copyright music users and distributes the money as royalties to the music creators. The service JACAP offers to right owners is monitoring the use of music in the territory of Jamaica, licensing the use of music for the purposes of public performance, broadcast, cable diffusion and recording, collecting licence fees or royalties for such use and distributing royalties.
Music Publishing is the business of protecting and promoting song copyrights and collecting the royalties that these copyrights generate. Think of a song as intellectual property (it's an original piece of art!), and music publishing as the business that makes sure that songwriters get paid a fair compensation when their intellectual property is used by companies. Those companies could be record labels (mechanical royalties), radio stations, bars, and restaurants (performance royalties), or film studios and advertising agencies (sync license fees), and many more.