Yes, CCC is working at a much lower level than you as a logged in user. Your harddrive most likely has two partitions. One for recovery and one for your working OSX installation. You as a user cannot copy your recovery partition to a new disk. CCC can do this or the OSX installer can create this. Someone could be using bootcamp and have other partitions on their drive that can’t be copied. APFS complicates this even further with its containers. The operating system has tons of hidden files and directories that you won’t see. As part of the security and system protection at lot of those files have special permissions on them that you would not be able to duplicate on the target system as a regular user. Someone could have multiple user accounts on their Mac. By default, you are only going to see your account’s data. OSX uses symbolic links for files, so you could potentially copy the link but not the actual files where they are actually stored.
As I said earlier, for just your data, you could copy from one drive to another without issue. Even then some of that is a little tricky with things like email, photos, iTunes data, iMessages, etc. But system files are a different story.
My best recommendation would be to clone your existing harddrive to your external drive, do a fresh install of OSX on your new iMac, and then run migration assistant to move your user data and applications onto the new iMac.