If files are copied from a first volume to a second volume, will the files stay the same?

When I connect the external hard drives to my computer(with FreeBSD or other Unix systems) and copy files from the first external hard drive to the second hard drive, are the files on the second hard drive the same as the files from the source (first external hard drive)? I know there is a hash (checksum). I read somewhere that copying from different volumes will result in different files(since they are 2 different volumes). Only when I copy a file to the same volume, I can guarantee it is the same file. **What is the recommendation for copying, and will my files stay the same?**