From a strict interpretation, the Bible Students were the followers of Russell and, when Rutherford hijacked the group, they left and continued following Russell's teachings. So, technically, the JW's are the splinter grouop of the Bible Students. Here's what the Bible Students have to say about that:
http://www.biblestudents.net/faq/questions.htm
"Isn't Charles Taze Russell the Founder of the Jehovah's Witnesses?
That is a misconception. Pastor Russell was the organizer of the International Bible Students Association. It was this loosely formed association that helped published the [Zion's] Watch Tower and Herald of Christ's Presence journal, and the [Zion's] Watch Tower Society.
This Society was an organizer of Bible Student conventions and other activities, but it did not dictate any creeds or rules to the independent congregations.
After Pastor Russell's death, The Watch Tower Bible and Tract Society began to rise as a hierarchy over the once independent congregations. Many refused to surrender their Christian liberty and here started the work of separation. As early as 1917 this exodus from the Society began, and those who appreciated the wonderful harmony of the Bible as taught by Pastor Russell are today known as Associated Bible Students.
By 1930, the Society no longer resembled that of its former self. Many Bible Students abandoned the Society, and by 1931, the name "Jehovah's Witnesses" was adopted by the new leadership to differentiate between the Society's Bible Students and those independent of the Society. "