Kamma, volition and tanha are three words for the same thing: the drive to become, to be-- "I-making." At least according to the Suttas.
PTS: A iii 410
Nibbedhika Sutta: Penetrative
"Intention, I tell you, is kamma. Intending, one does kamma by way of body, speech, & intellect.
Best explanation I ever found to explain the relationship/equality of these three terms is in Ven. Dr. Walpola Rahula's What the Buddha Taught.
In fact I went ahead and did the work. Here's the very passage:
Of these four, the last mentioned 'mental volition' is the will to live, to exist, to
continue, to become more and more. It creates the root of existence and continuity,
striving forward by way of good and bad actions (kusalakusalakamma). It is the
same as 'Volition'(cetana). We have seen earlier that volition is karma, as the
Buddha himself has defined it. Referring to 'Mental volition' just mentioned above
the Buddha says: 'When one understands the nutriment of mental volition one
understands the three forms of 'thirst'(tanha)'.
Thus the terms 'thirst', 'volition', 'mental volition' and 'karma' all denote the
same thing : they denote the desire, the will to be, to exist. To re-exist, to become
more and more, to grow more and more, to accumulate more and more. This is the
cause of the arising of dukkha, and this is found within the Aggregate of Mental
Formations one of the Five Aggregates which constitute a being.
Here is one of the most important and essential points in the Buddha's
teaching. We must therefore clearly and carefully mark and remember that the
cause, the germ, of the arising of dukkha is within dukkha itself, and not outside; and
we must equally well remember that the cause, the germ, of the cessation of dukkha,
of the destruction of dukkha, is also within dukkha itself, and not outside.
Which I think is one of the best passages I've ever read.
How it connects to belief: isn't "belief" an intentional act? Do --or do we not -- choose our beliefs? I will tell you that in a conversation with arch-skeptic Dr. Ray Hyman he absolutely astounded me (not an easy thing to do BTW) by flatly stating to me, "I have no control over my beliefs."