Greetings maddiejoanna,
Welcome to Apple Support Communities and congratulations on your new iPhone! Getting a new iPhone is very exciting.
I see that you have uploaded music from CDs to your iTunes library over the years, and after you restored your iPhone, many of the songs are different versions than the originals. You'd like to disable iTunes Match (or, potentially, iCloud Music Library as they provide similar functionality) and get the original songs back. I completely understand. I want to help you get your original songs back.
You'll need to disable iTunes Match, iCloud Music Library, or both as necessary in iTunes and on your iPhone. The following articles will help you locate the iTunes Match and iCloud Music Library setting on each device. Just make sure that you are turning each off:
Use iTunes Match on your computer, iPhone, iPad, or iPod touch
Use your Apple Music membership to get your music on all of your devices
Additionally, should you prefer not to use these services, you can use the following page to verify that the necessary subscriptions have been cancelled:
View, change, or cancel your subscriptions
Best Regards.