Okay dude, think of it like this. There is no exact translation, but basically Budo means, "warrior way" where as Bujitsu means "warrior art".
Historically and culturally, the martial arts of Japan can be divided into two areas: gendai budo and koryu
Koryu are all the old/ancient Japanese martial arts like kenjustu, the old style Japanese jiu-jitsu schools/ryus, tantojustu, aiki-jutsu. Stuff like that, generally any martial art style ending in a -jitsu/jutsu prefix is an older style of Japanese martial art when the samurai were concerned primarily with just straight up killing yo ass. It is much more combat oriented.
After Japan was unified by the Tokugawa shogunate and he laid a strong pimp hand down across the land, there really wasn't that much fighting anymore. Samurai weren't so much running around trying to kill each other anymore, but they still wanted to preserve their martial ways. It was during this time that a lot of the -do arts started to pop up, such as kendo (Japanese fencing). Take it one step further, after Japan was openned up to the West by Commodore Matthew Perry (think "The Last Samurai") the samurai were looked at as this relic of the past, and eventually men were forbidden to wear swords in public. More and more of the old -jitsu/jutsu arts began to be practiced/taught less and less and more of an emphasis was placed on "martial ways" than "martial arts", in other words training for physical/spiritual/mental development rather than just learning how to straight up kill someone on the battlefield.
Whenever you see some 49th grandmaster in some obscure Japanese jiu-jitsu or sword art, chances are very good it is a -jitsu/jutsu art and thus could be termed "bujitsu".
Your modern Japanese "budo" arts are kendo, judo, kyudo, iaido, stuff like that. They aren't necessarily "softer" martial arts, emphasis just isn't placed on killing someone.
Go to any kendo school and ask them the difference between kendo and ken-jutsu (my good friend does kendo) and his sensei was like, "kenjutsu is for killing, just for killing".