To clarify, you can't just swap disks from PS4 to PS4 - each disk is mated to that particular PS4, and if you put it in another PS4 the only option you will be presented with is reformatting it.
In order to essentially transfer everything - saves, games, themes, apps, settings, etc. - from the old machine, you've essentially got two options:
1) Use the backup utility
to back up the old PS4 to an external drive, then restore from that backup on to the new PS4.
2) Connect the two PS4s together with an ethernet cable, and use the built-in transferring utility
My memory, from doing both, was that option 2) - which I did when I replaced my base PS4 with a Pro - was quicker, but that may have been because when I did the backup-and-restore thing I only had a USB2 drive.