Copying Files without redundancy?

When backing up files to an external drive, I end up overwriting the older versions of files that were previously backed up. Is there a way to copy files from one place to another, but just have files that have been changed to update?

Kind of like how Time Machine or Drop Box works. It just senses changed files and overwrites those, but doesn't recopy unchanged files.

Hope my question makes sense. Thanks!

Kkamin