bhava (kammabhava, upapattibhava) and jati

My understanding is:

• kamma-bhava - moment to moment turning of Dependent Origination (DO) within one lifetime
• upapatti-bhava - the turning of DO on a multi life time perspective

The latter is what relates to jāti. Past Fabrication due to Ignorance from the previous life creates a new body with sense faculties with associated consciousness to experience the world leading to jāti.

According to Visuddhimagga XVII.270, jāti arises due to kamma condition and decisive support condition.

Here is a more detailed explanation taken from Nyanatiloka's "Buddhist Dictionary" (part of the definition of paṭiccasamuppāda):

"Through the process of becoming is conditioned rebirth" (Bhava-paccayā jāti), i.e. through the wholesome and unwholesome kamma-process (kamma-bhava) is conditioned the rebirth-process (upapatti-bhava). The 2nd and 10th propositions, as already pointed out, practically teach one and the same thing, namely, that kamma is the cause of rebirth; in other words, that the kammical volition (cetanā) is the seed out of which springs the new life, just as from the mango-seed is generated the new mango-tree.

Hence, the 5 kammical causes (ignorance, etc.) of the past birth are the condition for the kamma-results of the present birth; and the 5 kammical causes of the present birth are the condition for the 5 kamma-results of the next birth (s. diagram). As it is said in Vis.M. XVII: "Five causes were there in the past, Five fruits we find in present life; Five causes do we now produce, Five fruits we reap in future life."

Now, just as in this process of continually changing mental and bodily phenomena, nothing can be found that would pass from one moment to the next moment, so also there is no enduring entity, ego, or personality, within this process of existence that would transmigrate from one life to the next (s. nāma-rūpa, anattā, paṭisandhi, khandha). "No being and no living soul passed from the former life to this life, and yet this present embryo could not have entered into existence without the preceding causes" (Vis.M. XVII). "Many things may serve to illustrate this fact, as for example the echo, the light of a lamp, the impression of a seal, or the image produced by a mirror" (ib.).

"Whosoever is in the dark with regard to the conditionally arisen things, and does not understand that kamma originates from ignorance, etc., he thinks that it must be his ego that knows or does not know, acts and causes to act, and that arises at rebirth. Or he thinks that the atoms, or a creator, with the help of this embryonic process, must have formed this body, or that it is the ego endowed with faculties that has impressions, feels, desires, clings, continues and enters again into existence in a new birth. Or he thinks that all beings have been born through fate, or fortuitously" (Vis.M. XVII).

Now, on hearing that Buddhism teaches that everything whatever in the world is determined by conditions some might come to the conclusion that Buddhism teaches some sort of fatalism, and that man has no free will, or that will is not free.

The problem 'whether man has a free will' does not exist for, the Buddhist, since he knows that, apart from these everchanging mental and physical phenomena, no such entity as 'man' can be found, and that 'man' is merely a name not relating to any reality. And the question, 'whether will is free', must be rejected for the reason that 'will', or volition, is a mental phenomenon flashing forth only for a moment, and that as such it had not any existence at the preceding moment. For of a thing which is not, or is not yet, one cannot, properly speaking, ask whether it is free or unfree. The only admissible question would be whether the arising of 'will' is independent of conditions, or whether it is conditioned. But the same question would equally apply also to all the other mental phenomena, as well as to all physical phenomena, in other words: to everything and every occurrence whatever. And the answer would be: whether will arises, or whether feeling arises, or whether any other mental or any physical phenomenon arises, the arising of anything whatsoever is dependent on conditions, and without conditions nothing ever can arise or enter into existence.

According to Buddhism, everything mental or physical happens in accordance with laws and conditions; and if it were otherwise, chaos and blind chance would reign. But such a thing is impossible and contradicts all laws of thinking. Cf. Fund. III (end).

It is actually pretty simple. Once you have identified "yourself" and equated it with an organism, you must have been born. Makes sense? If you don't think you are this organism, moreover, you don't think there is any "you" at all, the notion of birth no longer applies.