The difference between Kyujitsu and Kyudo is a common question. Not so much in Japan, of course, but in the West.
Basically Kyujitsu developed into Kyudo. It did so from a ancient tradition of yumi no michi, the way of the bow. The Japanese bow has since time immemorial been used in a sacred manner; first with shamanistic rituals and later in some temple dojo as a Way.
The bow in Japan has always been primarily a weapon of war, or in some instances for hunting animals. But the Japanese have always been more inclined to farming and fishing than hunting. But when times were peaceful the warriors would practice for sport, and the Japanese were great sportsman; this was not yumi no michi, but just warriors practicing for sport. Yumi no michi only applied to the sacred use of the bow.
In the 1700's Master Morikawa Kozan of Yamato-ryu may have been the first to publish his schools practice with the kanji for kyudo rather than kyujitsu. He wrote of the use of the bow as a Way to self discovery as opposed to just a warrior's weapon. Of course, as mentioned he had good tradition support for the use of the bow in this way. By doing so he began the process that continues today, of moving the use of the bow as A Way; no longer just for killing or technical sport, but for 'something' else. The something else may depend on who's holding the bow.
Today there are those using the bow as a sport, or a traditional warriors art, or a Way; or all of the above. In these cases few, in any I think, are using the bow to kill; so we call all these ways Kyudo.