I found there are two differences in number of factors in Dependent Co-arising (Paticca Samuppada).
1. Ignorance as the origin of suffering (12 factors)
I think this is the most known explanation of dependent co-arising (Paticca Samuppada) which consists of 12 factors.
Paticca-samuppada-vibhanga Sutta (SN 12.2)
Kaccayanagotta Sutta (SN 12.15)
Paccaya Sutta (SN 12.20)
Avijjapaccaya Sutta (SN 12.35)
Lokayatika Sutta (SN 12.48)
Bodhi Sutta( UD 1.1)
Upanisa Sutta (SN 12.23)
This sutta even extends more than the 12 factors we commonly heard:
1. Ignorance -> Fabrications
2. Fabrications -> Consciousness
3. Consciousness -> Name-Form
4. Name-Form -> Six Sense Media
5. Six Sense Media -> Contact
6. Contact -> Feeling
7. Feeling -> Craving
8. Craving -> Clinging
9. Clinging -> Becoming
10. Becoming -> Birth
11. Birth -> Stress & Suffering
12. Stress & Suffering -> Conviction
13. Conviction -> Joy
14. Joy -> Rapture
15. Rapture -> Serenity
16. Serenity -> Pleasure
17. Pleasure -> Concentration
18. Concentration -> Knowledge & vision of things as they actually are present
19. Knowledge & vision of things as they actually are present -> Disenchantment
20. Disenchantment -> Dispassion
21. Dispassion -> Release
22. Release -> Knowledge of ending
23. Knowledge of ending.
So there are 23 factors in total. I think this sutta put more emphasis on the origin of Knowledge of ending instead of origin of suffering.
2. Consciousness & Name-Form as the origin of suffering (10 factors)
These sutta only explain 10 factors exluding Ignorance and Fabrication (sankhara). Also, the origin factor, Consciousness is mutually co-dependant with the second factor, Name-Form. It's explained well in Nalakalapiyo Sutta (SN 12.67), they are both inseparable, when one is ceased, other is ceased too. But I can't found this mutual explanation on other sutta which explain for 12 factors.
Maha-nidana Sutta (DN 15)
Nagara Sutta (SN 12.65)
Nalakalapiyo Sutta (SN 12.67)
I can draw relationship of the 10 factors like this:
1. Consciousness <-> Name-Form
2. Name-Form -> Six Sense Media
3. Six Sense Media -> Contact
4. Contact -> Feeling
5. Feeling -> Craving
6. Craving -> Clinging
7. Clinging -> Becoming
9. Becoming -> Birth
9. Birth -> Stress & Suffering
10. Stress & Suffering.
Loka Sutta (SN 12.44)
This sutta, despite it tells the consciousness & Name-Form as origin of world (birth & suffering), the explanation of the cessation of the world starts from craving first, instead of Consciousness & Name-Form.
Now, from the remainderless cessation & fading away of that very craving comes the cessation of clinging/sustenance...
I think this sutta is somekind of an elaboration of 3rd noble truth:
"And this, monks, is the noble truth of the cessation of dukkha: the remainderless fading & cessation, renunciation, relinquishment, release, & letting go of that very craving."
I would like to hear your explanation about this discrepancy.