I'm going to assume they aren't in the same folder.
That or they really don't have the same filename, but look like they do because extensions are hidden (a setting in Folder Options)
You can't have two files in the same folder with the same filename. The file system won't allow that to happen. It can be done with some trickery, but if you knew that trickery, you'd know how to copy the files, as well.
Bottom line: If the files are in different folders, copy both folders. Done.
If they are in the same folder, then the files are different times (one FILE.JPG and FILE.MP3 for example). You should be able to copy both those files together using drag & drop.
If you've got some other condition, then you've likely got a problem.
Have you looked in the FAQ yet?
How about the Wiki?
Under normal circumstances, a signature would go here.