Is there a difference in these two terms as to there philosophies?
First off I'd say that the Budo and Bushido have identical spiritual goals: to produce someone that's mastered themself, the difference is in intent for that self mastery.
Budo has no martial intention. Bushido uses self mastery for purely martial reasons. You can be doing both at the same time though and that's Aikido, in some places.
For example, Kendo is budo but kendo has no practical martial application, it's just use of a martial style system to produce non-martial goals. So there is no intention in Kendo to produce a competant fighting man or woman, there is no martial intention behind it, self mastery is the goal.
Aikido, in some dojo anyway, is two fold, either by design or by accident. Whatever the intentions of O-Sensei there are people that study it and teach it for self defence, there is at least in places in the Aikido world, a martial intent it's not just a tool for making nice people.