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In Pali, there are at least two words translated as 'arise':
The 2nd type of arising (uppajjati) pertains to the five khandhā arise in connexion with each of the six āyatanāni. All this means is the five aggregates are known/experienced by the sense bases. This is not related to Dependent Origination.
Per SN 22.5 quoted above or MN 9 or MN 28 (below), samudaya is Dependent Origination.
“One who sees dependent origination sees the teaching.
“yo paṭiccasamuppādaṁ passati so dhammaṁ passati;
One who sees the teaching sees dependent origination.”
yo dhammaṁ passati so paṭiccasamuppādaṁ passatī”ti.
And these five grasping aggregates are indeed dependently originated.
Paṭiccasamuppannā kho panime yadidaṁ pañcupādānakkhandhā.
The desire, clinging, attraction and attachment for these five grasping aggregates is the arising of suffering.
Yo imesu pañcasu upādānakkhandhesu chando ālayo anunayo ajjhosānaṁ so dukkhasamudayo
Uppajjati is not Dependent Origination because when the cessation of Dependent Origination occurs, uppajjati still arises & occurs, as follows:
Eye consciousness arises (uppajjati) dependent on the eye and sights. The meeting of the three is contact. Contact is a condition for the arising of what is felt as pleasant, painful or neutral. When you experience a pleasant feeling, if you don’t approve, welcome and keep clinging to it, the underlying tendency to greed does not underlie that. When you experience a painful feeling, if you don’t sorrow or wail or lament, beating your breast and falling into confusion, the underlying tendency to repulsion does not underlie that. When you experience a neutral feeling, if you truly understand that feeling’s origin, ending, gratification, drawback and escape, the underlying tendency to ignorance does not underlie that. Mendicants, after giving up the underlying tendency to greed for pleasant feeling, after dispelling the underlying tendency to repulsion towards painful feeling, after eradicating ignorance in the case of neutral feeling, after giving up ignorance and giving rise to knowledge, it’s quite possible to make an end of suffering.
On seeing a form with the eye, he does not lust after it if it is pleasing; he does not dislike it if it is unpleasing. He abides with mindfulness of the body established, with an immeasurable mind, and he understands as it actually is the deliverance of mind and deliverance by wisdom wherein those evil unwholesome states cease without remainder. Having thus abandoned favouring and opposing, whatever feeling he feels, whether pleasant or painful or neither-painful-nor-pleasant, he does not delight in that feeling, welcome it, or remain holding to it. As he does not do so, delight in feelings ceases in him. With the cessation of his delight comes cessation of clinging; with the cessation of clinging, cessation of being; with the cessation of being, cessation of birth; with the cessation of birth, ageing and death, sorrow, lamentation, pain, grief, and despair cease. Such is the cessation of this whole mass of suffering.
In summary, SN 12.48 refer to two types of five khandha:
The mere five khandha arise (uppajjati) in connexion with each of the six āyatanāni.
The five aggregates subject to grasping arise (samudaya) in connexion to ignorance, craving & grasping.