Recording (or tracking) is just what it says, you're recording something. In music, it would be a performance; vocals, instruments, etc. Sometimes each instrument or vocal is recorded by itself and sometimes they might be recorded together.
Mixing is when you have several recorded tracks and you want to put them together to make a song. This is where you set levels, eq, reverb, delays, compression, or whatever is needed to get the different recorded instruments and vocals to sound like they were recorded together.
Mastering is when you take several songs and make small adjustments to get them all to sound similar as a cohesive album. Then make a master copy that can be sent to a reproduction facility mass production.
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