Are you referring to libraries, like My Music & Public Music? If you right-click on My Music and choose properties then select the Location tab, it will show you the actual folder where the music is stored. If you do the same on Public Music and it is a different location then yes you stored the files in two places. If you want your files to be accessible to any user that logs on then you can store them in Public otherwise store them under "My _____". If you are the only user who will ever log on then you have no need for public.
Normally there are sample files in public but not your own files unless you copied them there. I suggest an experiment to first verify you have two distinct copies and not simply two libraries pointing to the same folder; delete a single file from Public _____ and then go over to My _____ and see if the file is still there. If it is there open it just to be sure it works, then yes you have two distinct libraries and can remove the files from Public; if it is NOT there then go to Recycle Bin and restore the file.
If you do not want the public folders then first make sure you have everything out of them that you want in your My folders; then delete all the files (or all the files but sample) and then right click on public _____ and choose Remove Location From Library. Remove location from library does NOT delete the public folder it merely removes the link/pointer from libraries; that is why you must delete any duplicate files you created, first.
