buddha may teach the same topic by the difference words for one from the northern and another one from the southern

The answer of this question

According to your quote, khayāya and nirodha mean same. It is synonym of each other for that context.

There are two suttas, one about destruction of craving and other about the cessation of craving.

Why buddha teach those both sutta by those difference words in the same meaning?

Because some word is understandable just for some listener. Similitude, if you say "give me barbie" in the Australian's restaurant, it may means "give me barbecue", not barbie doll, because "barbie" is a slang of barbecue in Australia. Also, buddha may teach the same paṭiccasamuppāda by the difference words for one from the northern and another one from the southern, because of their lingo.

Then how to know they are the same?

1. Your quote suttas come together, the first is full, but the next is brief. That means the 1st saṅgāyana-members decided to brief the next sutta because of the previous sutta.
2. The other sutta, which describing paṭiccasamuppāda as alike as your quoted sutta, use these 2 words as each other synonym, such as in Sutta. Saṃ. Ni. parivīmaṃsanasutta:

ayaṃ vuccati bhikkhave bhikkhu sabbaso sammā dukkhak-khay-āya paṭipanno jarāmaraṇa-nirodh-āya.
This is called a mendicant who is practicing (paṭipanno) for(āya) the complete ending (khaya) of suffering (dukkha), for(āya) the cessation(nirodh) of old age and death (jarāmaraṇa).
[jarāmaraṇa=dukkha follow to SN Dhammacakkappavattanasutta and SN Paṭiccasamuppādavibhaṅgasutta]

There are another example of the same case in Vinaya. Mahāvi (1) Paṭhamapārājikakaṇḍaṃ as well

The side answer in this question

It is very easy to take two piece of jigsaw, then say "whole of jigsaw-pieces in this box is not united, because these 2 pieces can not connect together". And people who addicts drama-movie often love&like to act like this.
But it is uncountable hard to relate and connect a thousand pieces of jigsaw together by the right way. It is harder when that jigsaw has changed the box more than 2,600 times through 2,600 years.
However, if one in 2,600 years later can done that jigsaw to be unity. It's means the fist box owners already marks the numbers at each piece of jigsaw very clearly, and they also wrote the manual "how to connect the jigsaw together", then sent it from the previous generation the the next generation for 2,600 years.

According to Dhammadhatu's answer:

I was once taught the Pali word "atthaṅgama" refers to a temporary cessation where as "nirodha" refers to a permanent cessation.

Atthaṅgamo can refer to a permanent cessation, too. Such as in DN Nidāna. Dukkasuttaṃ:

10. “Monks, what is the fading (Atthaṅgamo) of unpleasantness?
11. “Monks, on account of eye and forms arises eye-consciousness. The coincidental arising of the three is contact. On account of a contact are feelings. On account of feelings is craving. With the cessation of that craving without a remainder holding ceases. With the cessation of holding being ceases. With the cessation of being birth ceases. With the cessation of birth, decay, death, grief, lament, unpleasantness displeasure and distress cease. Thus ceases the complete mass of unpleasantness.

According to Dhammadhatu's answer:

Therefore, I think the suttas should be researched to affirm or refute this idea that "nirodha" refers to a permanent cessation.

Sāriputta already done it, but the anti-abhidhammist often ignore it. So, according to Ven. Payutto and Sāriputta-mahāsāvaka, there are 5 type of cessations using in tipitaka that appears in various difference words:

[224] Nirodha 5 = extinction; cessation of defilements.

1. Vikkhambhana-nirodha — extinction by suppression.
2. Tadaṅga-nirodha — extinction by substitution of opposites.
3. Samuccheda-nirodha — extinction by cutting off or destruction.
4. Paṭipassaddhi-nirodha — extinction by tranquillization.
5. Nissarana-nirodha — extinction by escape; extinction by getting freed.

These example words have the same meaning as well: Pahāna 5 (abandonment 5), Vimutti 5 (deliverance 5), Viveka 5 (seclusion 5), Virāga 5 (detachment; dispassionateness), Vossagga 5 (relinquishing), etc.

Actually, atthakathā already researched and often specified one of these 5 meaning for each nirodha-word found in each sutta. But the anti-abhidhammist ignore them, never try to study abhidhamma and atthakathā as they are and by the ancient study system. So although the research already done, they still never know the existence of that research.

According to Dhammadhatu's answer:

The word "kkhayo" ("destruction") definitely refers to a permanent cessation or "uprooting". When the Buddha 1st uttered his awakening, he referred to the destruction of craving

1. There is no kkhaya-word in pāli. Pāli has only khaya. But -k- of taṇha*-k-khaya (taṇha+khaya) is a word merging as alike as -t- of get-t-*ing (get+ing).
2. Khaya not used only as a permanent cessation, there are many khaya used as temporary cessation, such as in Sutta. Saṃ. Kha. Ānandasutta:

4. “Ānanda, matter is impermanent, compounded and arise dependently and it is of the normal of withering(khaya), fading (vaya), loosing interest (virāga) and ceasing (nirodha[temporary]). The cessation(nirodha[permanent]) of that is cessation.

According to Dhammadhatu's answer:

Another contra argument against synonymity is it is impossible for "kkhayo" ("destruction") to be used in Paticcasamuppada because "nirodha" in Paticcasamuppada refers to the extinguishing of ignorance that taints consciousness, mind-body, sense bases and contact rather than the destruction of consciousness, mind-body, sense bases and contact.

Kaya-word was not directly used in Paṭiccasamuppādavibhaṅgasutta. But Kaya-word was used instead of cease-word, (nirodha-paṭiccasamuppāda) directly in various suttas and in many relation with paṭiccasamuppāda, such as:

“Sir, a mendicant who is perfected—with defilements ended, who has completed the spiritual journey, done what had to be done, laid down the burden, achieved their own goal, utterly ended the fetters of rebirth, and is rightly freed through enlightenment—is dedicated to six things. They are dedicated to renunciation, seclusion, kindness, the ending of craving, the ending of grasping, and mental clarity (no-ignorant).
“Yo so, bhante, bhikkhu arahaṃ khīṇāsavo vusitavā katakaraṇīyo ohitabhāro anuppattasadattho parikkhīṇabhavasaṃyojano sammadaññāvimutto, so cha ṭhānāni adhimutto hoti— nekkhammādhimutto hoti, pavivekādhimutto hoti, abyāpajjādhimutto hoti, taṇhāk-khayā-dhimutto hoti, upādāna-kkhayā-dhimutto hoti, asammohādhimutto hoti.

According to Dhammadhatu's answer:

Also, the term "tanhanirodha" appears to be not found in any other sutta, apart from in suttas about dependent origination.
This gives rise to two different conclusions:

1. SN 46.27 is a fake sutta. Generally, when "permanent nirodha" is referred to, the term "asesa" ("remainderless") is also included. Since SN 46.27 does not include the term "asesa", it could be a fake sutta.

The fact is: only in the cessation noble truth that taṇhā-nirodha come with "asesa" as "yo tassaāyeva taṇhāya asesavirāganirodho" . even in Paṭiccasamuppādavibhaṅgasutta "asesa" come with only avijjā as "avijjāya tveva asesavirāganirodhā". But taṅhā come with nirodha without "asesa".

When craving ceases, grasping ceases.
taṇhānirodhā upādānanirodho; (no "asesa")

Actually, we all know that the meaning of "asesa" also included by the context relation. But, it was fail, if someone said 'when "permanent nirodha" is referred to, the term "asesa" ("remainderless") is also included'.
So, this fail can not prove "it could be a fake sutta."

According to Dhammadhatu's answer:

2. SN 46.27 explains how to achieve the "cessation" mentioned in SN 46.26; upon which the factors of enlightenment depend on. In other words, the "destruction" in SN 46.26 is about final Nibbana where as the "cessation" in SN 46.26, which the factors of enligthenment are dependent upon, is the non-final cessation from starting the Path.

The fact is: If one think 'SN 46.27 has to have "asesa" to be "final Nibbana"'. According to that idea, SN 46.26 can not be "final Nibbana" as well, because AN 46.26 also doesn't have "asesa" as well.
So, this fail can not prove "it could be a fake sutta.", because the logic are fail at both.

According to Dhammadhatu's answer:

Therefore, the respective terms "kkhayo" and "nirodha", as used in SN 46.26 and SN 46.27, may not be synonymous.

Therefore, those all reasons can not prove '"kkhayo" and "nirodha", as used in SN 46.26 and SN 46.27'.

So, what happen in SN 46.26 and SN 46.27?

The possible case is "some of the listening-bhikkhu came form the other state, they didn't understand and did confuse of "khaya" in SN 46.26, while Buddha had be teaching. Because of that confusing, they couldn't memorize that sutta. Then they ask the buddha for repeat again "Please, repeat again, because I confuse of 'khaya'-word in 'taṇhakkhayā kammakkhayo kammakkhayā dukkhakkhayoti', so I can't memorize this sutta". Then the buddha know and repeat as SN 46.27.