They are just the synonym.
- Sakkāya is an object of anu-diṭṭhi. So, sakkāyadiṭṭhisutta and
attānudiṭṭhisutta have the same content. This is the english translated version of those suttas,
attānudiṭṭhisutta is next of sakkāyadiṭṭhisutta.
Your 3 suttas,
which near by each other, describing each other like this:
Diṭṭhi means misunderstanding of causes and effects, clinging-aggregates which is anattā as
attā.
Anu is prefix which means often.
Micchā is prefix which means mistake.
Sakkāya is a name of clinging-aggregates follow to many sutta, such as Sutta. Ma. Mū.
Cūḷavedallasuttaṃ.
These clinging-aggregates are the Sakkāya described by the Blessed One.
So,
sakkāya-micchā-anu-diṭṭhi means
often mis-understanding, micchā-anu-diṭṭhi (verb act as noun),
of sakkāya (object), causes and effects, clinging-aggregates anattā as attā.
Note1: Sakkāya is not only internal, because there are internal clinging-aggregates, internal sakkāya, and external clinging-aggregates, external sakkāya, which are contemplating by the practitioner in
Cūlavedallasutta and Sutta. Ma. Mū. Sacca-pabba of
Satipaṭṭhānasuttaṃ (<< this link is a good translation of this sutta).
they meditate by observing an aspect of the principle inside and outside.
The inside and outside aspect of the principle in this term is sakkāya (clinging aggregates), sakkāyasamudayo, sakkāyanirodho, and sakkāyanirodhagāminīpaṭipadā.
Note2:
Santo kāyo sakkāyo. Kāya, clinging-aggregates, is sacca, santa, vijjānana, the reality, truth, possible to arise in causes and effects cycle. So, buddha said sakkāya is sacca and clinging-aggregates in Sutta. Saṃ. Kha.
Sakkāyasutta[trans].
"Sakko kāyo sakkāyo" and
"para kāyo sakkāyo" is allowed in Ma. Mū. Sacca-pabba of
Satipaṭṭhānasuttaṃ as an internal anupassī,
but it is not the primary meaning when compare to Sutta. Saṃ. Kha. Sakkāyasutta[trans], which sakkāya meaning is defined by buddha directly. And "para kāyo sakkāyo" never found in any where else except in Satipaṭṭhānasuttaṃ.
So, if you use
"sakko kāyo sakkāyo" in
Sakkāyasutta, Sakkāyasutta, which has only
sakko, will conflict with Sacca-pabba of
Satipaṭṭhānasuttaṃ, which has
both sakko and paro.
But by the
"Santo kāyo sakkāyo", there is no conflict like that between the
co-context sutta, such as
micchādiṭṭhisutta,
sakkāyadiṭṭhisutta, and
attānudiṭṭhisutta, which using the same context and
near by each other.
Also, there is no conflict between those sutta and the faraway suttas such as Sutta. Saṃ. Kha.
Sakkāyasutta, Sutta. Ma. Mū. Sacca-pabba of
Satipaṭṭhānasuttaṃ, and Sutta. Ma. Mū.
Cūḷavedallasuttaṃ.
Note3: Your 3 suttas,
which near by each other, describing each other. Mostly words of them can use in the other sutta, such as anicca, dukkha, anatta, of these 3 sutta contexts all refering to saṅkhata (clinging-aggregates), which means arisen by causes. So, it can use to explain each other like appeared in Vinaya. Mahā (1)
Anattalakkhaṇasutta:
- ‘Now what do you think, O bhikkhus, is the body permanent or perishable?’
‘It is perishable
(anicca), Lord.’
‘And that which is perishable, does that cause pain or joy?’
‘It causes pain
(dukkha), Lord.’
‘And that which is perishable, painful, subject to change, is it
possible to regard that in this way. ‘This is mine, this am I, this is
my self
(atta)?’ ‘That is impossible, Lord.’