Glossary -- RealMode 16 bits Operating mode in which the x86 cpu runs when it boots. That mode is mainly for backward compatibility and provide very few help for the modern developer (no memory protection, only 1MB of adressable memory, no virtual memory support). BIOS and DOS are typically real-mode stuff. All the rest you know (windows, linux, DukeNukem3D, zsnes, dos4gw, djgpp ...) are ProtectedMode OS/applications/dosextenders respectively.
additionnal informations about address formations in RealMode can be found in Perica's tutorial on 
Bona Fide.