Master recordings are the recordings of the performance of your music that you make money off of by selling copies via CDs, on iTunes, etc. You can make money off of master recordings by selling your own recordings directly to your audience (make your own CDs and sell them at your shows, or use CD Baby to distribute your master recordings digitally through music stores like iTunes), or by signing a deal with a record label that will help you make your master recordings and sell them to the public.
Music publishing refers to the money you make from government mandated royalties that must be paid to you when other people or companies use music that you wrote, also referred to as the composition. That can refer to your record company making a copy of your music (mechanical royalties), when a radio station, website, or restaurant plays your music to help them make money (public performance royalties), or if a television show or film uses your music in their productions (sync royalties).

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