Yum, or the Yellowdog Updater Modified, is a package manager for RPM-based distributions; DNF, sometimes referred to as Dandified Yum, is the next generation of that package manager.
Yes, for the most part DNF usage is very similar to yum’s. Additional information on DNF detailing the similarities, and differences, will be available in the Liquid Web Knowledge Base very soon.
DNF has been the default package manager for since the 22nd version of Fedora, Fedora 22. Dandified Yum was introduced in Fedora 18.
Yum has long been considered a poor performer. It was notorious for high memory usage, and the slowness when resolving dependencies. DNF now uses libsolv, an external dependency resolver, and hawkey for resolving dependencies, while yum used its own, internal, dependency resolver.