If you look in the android apps store, there are backup applications. I use "App Backup Reinstaller." It's not fantastic, but I've used it to back up my apps to an SD card, then backed up my data directories to the SD card, removed the SD card, did a factory reset, and re-installed from the SD card. My apps were there, my settings were there, and my data was there. The data was from a copy as you described above, not from the backup.
If you have rooted your device, you may be able to back up everything with just a copy, but I do not root so I can't tell you.