Koryu budo is yet another term--along with kobudo, kobujutsu, and koryu bujutsu--used in Japan to refer to the classical martial traditions. Budo, strictly speaking, refers to a Japanese martial way, while the modifier "koryu" distinguishes the classical or traditional martial arts from the modern, or gendai systems (see the "Koryu Primer" and "The Meaning of the Martial Arts: Some Reflections Along the Way" for more detail for more on -do versus -jutsu and koryu versus gendai). So koryu budo may be translated as "classical martial way".
Kobudo means simply "old" (ko) "martial way" (budo). Although this term appears more often in the West associated with Okinawan weapons systems, in Japan it is equally likely to refer to the classical warrior traditions. For example, the top two organizations of classical martial arts in Japan, the Nippon Kobudo Shinkokai, and the Nippon Kobudo Kyokai, both refer to the arts they represent as "Kobudo". In the same vein, kobujutsu refers merely to "old" (ko) "martial arts" (bujutsu).
Does it really matter which term a Japanese martial art outside of Japan uses? To the Japanese, absolutely not. The terms are used interchangeably, with budo the most frequently heard. Bujutsu might possibly be used to distinquish an art with a stronger emphasis on combative technique from those that focus on life discipline (the "Way"), but in general, budo is the term used in Japan to refer to martial arts.
So to answer the question: "What's the difference between koryu budo, kobudo, kobujutsu, and koryu bujutsu?" For all practical purposes, there is none.