iTunes Store and iTunes [for Windows or Mac] are entirely different. iTunes Store is Apple’s media store where you can purchase and download media to your iPad. Downloaded music is accessed using the Music App on your iPad.
Note that you cannot export media that you have “purchased” to other devices. In purchasing copyrighted media from Apple, you have purchased a “licence” to listen to the material. You do not own the media or its copyright.
You can however, synchronise media stored on your Apple devices via a Windows PC (with iTunes for Windows installed) or a Mac computer (with iTunes or Finder - as appropriate for the installed version of macOS).