Although there is really no wrong answer here, as this is about how or if the terms affect you outside the dojo, I just thought that a little clarification might be in order.
Actually, the terms Budo/Bushido aren't all the different from each other. Donn Draeger was the one who popularized the opposition between these terms in the West, but at this point the consensus is that it is a false dichotomy. In other words, some Koryu reffered to their philosphy as 'bushido' others as 'budo'. That's why I just put a slash (/) between them.
That being said, there is difference between 'Gendai Budo' and 'Koryu Bujutsu'. Gendai Budo here refers to an art that was created after the Meiji Restoration, whereas Koryu Bujutsu, refers to those that were created before it.
So in a way your not far off the mark. Gendai Budo is kind of about self defense and personal growth, whereas Koryu Bujutsu is directly concerned with killing your enemies (although there is a large body written about personal growth via the martial arts prior to the Meiji Restoration).
Finally, Budo as a philosophy isn't all that different from Bushido. The main difference, to somewhat over simplify it, would be that, for Bushido, the aim is personal growth to make you better on the battlefield. Whereas Budo is about personal growth for the sake of living an all around better, more introspective, life.
"Seek not to follow in the footsteps of the men of old; seek what they sought."