Okay, I’m obviously pretty bad in making jokes (“abhisutta” seemed really hilarious at the time it popped into my head), so I’ll stick to the serious discussion:
I think we have to be careful about the context when using different terms like “sutta, dhamma, abhivinaya” etc.
For example, as mentioned before, please remember the “ninefold dispensation”, i.e. what constitutes “dhamma”. If you don’t trust the commentary, here's the same thing from MN22 for example:
"Here, bhikkhus, some misguided men learn the Dhamma - discourses, stanzas, expositions, verses, exclamations, sayings, birth stories, marvels, and answers to questions - but having learned the Dhamma, they do not examine the meaning of those teachings with wisdom."
The pali for the above 9 divisions of the Dhamma is:
sutta, geyya, veyyakarana, gatha, udana, itivuttaka, jataka, abbhutadhamma, and vedalla.
So by that definition, gatha certainly isn’t a subset of suttas. Accordignly, there’s no “abhidhamma” in the above nine angas, so to say that abhidhamma is a subset of suttas is also confusing. According to the commentary, the stuff that abhidhamma pitaka is made of seems to fall under “expositions” - “veyyakarana”. Here’s that Atthasalini quote again (please notice the veyyakarana term in both the above sutta and below commentary quotes):
"Thus as rehearsed at the council, the Abhidhamma is Pitaka by Pitaka classification, Khuddaka-Nikaya by Nikaya classification, Veyyakarana by part classification and constitutes two or three thousand untis of text by the classification of textual units"
Of course, it would be great if that Vinaya IV, 344 quote said, “study suttas, gathas and veyyakarana” as then we would know exactly what context it’s referring to, but instead it says “study suttas, gathas and abhidhamma", so it’s a bit uncertain from a scholarly point, but it seems unlikely (to me at least) that the context for the Vinaya quote refers to the following classification (which seems closer to what retro and David advocate, though still wider):
There is a classification when “sutta” is really meant to stand for more than just suttas of the ninefold division: I asked on DSG list about the term “sutta and vinaya”, this is a reply (post #100522) by robertk quoting Ven.Dhammanando (please notice that “sutta” includes all 3 pitakas, while “dhamma” is even wider!):
Sometimes the terms 'sutta and vinaya', sutta means Dhamma as whole.
Venerable Dhammando explained:
Dhammanado: They are:
"1) The "well-said" (sutta), defined as the whole of the Tipi?aka.
2) The "conforming to the well-said" (suttanuloma), meaning utterances than can
be shown to be Dhamma or Vinaya by using either of the two sets of four great
3) The "disquisition on meaning", "commentary" (atthakatha), meaning the works
preserved in Sinhalese that the Mahavihara commentators used as their source
texts. The contents of these were held to date from the First Council, and so
were viewed as authoritative unless contradicted by sutta or suttanuloma.
4) The "personal opinion [of an acariya]" (attanomati), said to be the weakest
source of authority""
end quote by Dhammanando
So anyway, let’s be a bit more careful about the context for the sake of clarity.