Hi David, I am approaching as an end user of software. Some Linux software vendors say that their software is supported on Ubuntu.
If I am running Debian or Mint, which are similar to Ubuntu, and I install the package. I think Ubuntu is still using the standard .deb package format thru apt-get? Should I expect it to work or fail most of the time?
In addition to what davidktw has stated, note that Debian, Ubuntu and Linux Mint have different approaches to configuration files location/naming as well as package names.
The Apache web server package is the best example of this, some distributions use a centralized httpd.conf file and name the service httpd, while other distributions split the configs into different folders and use a2enmod/a2dismod/a2ensite/a2dissite to manage them.
I think Debian and Ubuntu ideology on this has diverged (memory is a bit rusty as I am using Debian and Nginx mainly).
But basically if you are an end-user, I suggest not mixing and matching packages from differing distributions (e.g. CentOS/RHEL<>Fedora<>Mandriva too) because the packages will install, but the file locations and scripts may not adhere to the distro's ideologies and scripts (the distro's "way of doing things").