The practical difference is the package manager; Debian-based systems use dpkg/APT with the .deb package format, Arch uses Pacman with .pkg packages.

Debian-based distros use a stable release cycle, so there are version numbers. The ecosystem is maintained for each version for an extended period of time, so if you have a workflow that requires a specific era of software, you can stick with an older version of the OS to maintain compatibility. This does not necessarily mean the software remains unpatched; security or stability patches are applied, this tends to mean the system is stable. Arch-based distros use a rolling release, basically what they said they were going to do with Windows 10 being the "last" version of Windows and they'd just keep updating it. Upside: Newest versions of packages all the time. Downside: Newest versions of packages all the time. You get the latest features, and the latest bugs.

Debian-based distros don't have a unified method of distributing software beyond the standard repositories. Ubuntu tried with PPAs, which kind of sucked. Arch has the Arch User Repository, or AUR.

Arch itself is designed to be an a la carte operating system. It starts out as a fairly minimal environment and the user will install the components they want and only the components they want, though many Arch-based distros like Manjaro and EndeavorOS offer pre-configured images. Debian was one of the earliest distros shipped ready to go as a complete OS; I know of no system that offers the "here's a shell and a package manager, install it yourself" experience on the Debian family tree.

But given an installed and configured Debian and Arch machine, what can one do that the other can't? As in, can it run [application]? Very little.