Loss in quality of backup files?

If you save backup copies of files (jpeg or RAW) in a different location, is the quality of the copied files as good as the original?

I ask because I need to free up some space on my built in hard drive, but now that I have copied the files across to an external hard drive, the total number of bytes is a bit less. I also remember someone saying in the past that images lose quality when you save a copy, but she may have been referring to when you edit a jpeg, I can't quite remember.

I don't really want to delete the originals until I have clarified this. Thanks.