Biggest difference between Ubuntu and Pop is that Ubuntu aims to popularise usage of snap and uses apt as a backup option while Pop aims to deliver its software through apt and flatpaks, in the priority that the user wants.
Flatpaks are more consistent to run, they can run between all distros but install dependencies seperately so could take up more space for installations.
Apt makes use of the native debian installation, which works well for most but sometimes you could be stuck in a dependency hell between some software. Uses the storage more efficiently as it can share dependencies between multiple installed packages.
Snap sucks. There's literally no point in using it. It can run apps on all distros similarly to flatpak but its worse in every possible way. It hits noticably to run time of applications.