The package file, no matter if it's rpm, deb or something else, contains few things: Files for the software itself (executables, libraries, documentation, default configuration), depencies for other packages (as in to install software A you need also install library B) and installation scripts for the package. There's also some metadata, info for uninstallation and things like that, but that's mostly irrelevant for end user.

And then you need suitable package manager. Like dpkg for deb-packages, rpm (the program) for rpm-packages and so on. So that's why you mostly can't run Debian packages on Fedora or other way around. But with derivative distributions, like kubuntu and lubuntu, they use Ubuntu packages but have different default package selection and default configuration. Technically it would be possible to build a kubuntu package which depends on some library version which isn't on lubuntu and thus the packages wouldn't be compatible, but I'm almost certain that on those spesific two it's not the case.

And then there's things like Linux Mint, which originally based on Ubuntu but at least some point they had builds from both Debian and Ubuntu and thus they had different package selection. So there's a ton of nuances on this, but for the most part you can ignore them, just follow documentation for your spesific distribution and you're good to go.