Since Ubuntu is a Debian derivative I thought maybe it's possible
As mentioned, Ubuntu is really "source code derived", but since Ubuntu and Debian use slightly different compilers, kernels, and library versions, installing Debian packages on Ubuntu can result in a lot of weird behaviors (crashes, corruption, etc). That said, some things will work okay if the library interfaces are unchanged.
Ubuntu is derived from the Debian "unstable" branch, which is the in-progress and most up-to-date version of debian. If you tried installing a package from debian unstable, it might work, but there should already be an ubuntu equivalent that you should use instead. If you tried using packages from any of the older debian releases, you would be getting old versions and would run into dependency errors that would either stop you from installing or break your official ubuntu packages.
Check if there is an ubuntu PPA (personal package archive) for the package you are looking for - odds are someone else has already recompiled it for ubuntu and you can just use that instead.