It is almost always a very bad idea to install a package meant for one distribution on another.
It doesn't really matter if they use the same package format or not, but different package formats deter most users.
Packages usually have some dependencies that are set based on what is in the intended target distribution. A different distribution will have different versions of many of those dependencies, some will be usable, others won't.
Debian (and derivatives - I don't know the other formats well enough) packages (
.deb) can contain scripts that does things before/after installation/removal, those might fail or behave in strange ways if the target system is not as expected.