Trying to get one Library to snyc onto my iphone

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I have itunes on my computer, an iphone, and apple music. I have configured my itunes library ( only checking songs that I want to transfer to my iphone) I plug the phone into my computer to try to get the Library that's on my computer to go onto my phone.I push sync. But what happens is that I get songs on my phone but it is not a copy of the library that is on my computer. Maybe its pulling I library from the Cloud? If so how do I change it?