Difference between RPM (yum) and apt-get

They basically do the same, managing software packageges. One handles rpm packages which are the native form on Red Hat, Suse and Mandrake based systems (among others), the other handles deb files used by Debian, Ubuntu and derivatives.

My recommendation: Use the native format, except when you have very special needs. All the security updates etc. are best handled by the platforms native tool, and most users won't need to toy around with more than one tool.

As far as I know, RPM has an advantage in that it tracks dependencies by files included in packages, while Deb does this by package names and versions only. This means that if the new version of a package does not contain a shared library used by some other package, Deb system will install it and break that other package, while RPM-based systems will not install the new version.

On the other hand, RPM does not support OR-dependencies, common in Debs: this-package or that-package.