Actually, to be pedantic here, there is a tiny difference.
Yes, your pedantic note is correct. I'm using shorthand for air travel that "it doesn't matter what status you
hold if you don't have the required documents to prove it at the airport." Same for canadian citizens/passport holders.
But see below: you're spending time on corner cases and missing the main point.
But for example, a dual Canadian-Irish citizen and US green card holder who didn't have their Canadian passport ready could presumably fly into Canada just using their Irish passport and US green card without even bothering with the special authorization route, unless there's something I'm not understanding. I mean there might be a bit of a talk with the border officials once one gets off the airplane, but I'd think that this would be enough to get onto the airplane.
And then a person who wasn't Canadian at all - just an Irishman with a US green card - but who didn't have his green card ready, could he apply for an ETA if he wanted to (e.g. since he lost his green card or because he forgot it had already expired) and then fly into Canada on that? Or would Canada somehow know about his green card and thus deny the ETA? (Of course, even then special authorization then still wouldn't apply here since this person doesn't have Canadian citizenship.)
Your pedantry above is misplaced - you are missing a very important point.
A Canadian citizen [whose information is in the Canadian government's identifying databases]* will NOT be allowed to board a plane to Canada without a Canadian passport. That's the ENTIRE point of this discussion. They also are NOT eligible to get an ETA - it will be refused when they try to get one.
The only exceptions to this are Canadian citizens who are travelling on US passports - and those who get the special authorization above.
I don't think Canada gives a damn if an Irish citizen with a green card wants to apply for an ETA. I certainly don't.
* My caveat about 'whose information is in the government databases is important', but does not apply to most. The exceptions here might be those who are born abroad and not yet registered (which I refer to as 'presumptive citizens' - but it's a technical argument, they're
citizens by right but if the Canadian government has no record of that, well, you see the point). Probably some born-in-Canada but travelling on a different passport
and who have never applied for a passport or citizenship certificate. (As far as I'm aware, no, there's no automatic registration of newborns to some centralized citizenship database - and even if there is one now, it definitely does not apply to all those born in Canada and still alive).
And of course: any database system like this can have errors of various types. But it's pretty damn comprehensive and accurate, overall.
Make no mistake: except for these identified exceptions, Canadian citizens need a passport to board a plane to Canada.
[*Oh I know there's another big group that I don't know the nuances of, those covered under the Indian Act in Canada and some covred by the roughly-equivalent acts in USA. That's a whole separate special case, and can't be simplified into 'Canadian/USA citizens' so easily.]