You've misunderstood "how Flatpaks work": they are using the same system calls that containers use for containerization but in a different way, look at https://en.wikipedia.org/wiki/Linux_namespaces (Snaps use AppArmor too if that's a more familiar technology).

They are not containers in themselves: if you feel this is pedantic, the way namespaces are used can make all the difference (eg. why you should not be running stuff in docker containers as root which can easily be used to get root on the host).