I still think that the language property (or requirement, or behavior as seen by within the language itself) that we're talking about in this case is "unbounded nested calls" and that the language specs doesn't (shouldn't) assume that such property will be satisfied in a specific way, e.g. switching the call to a branch, as TCO usually means.
Unbounded nested calls as long as those calls are in tail position, which is a thing that needs to be defined—trivially, as `return EXPR(EXPR...)`, in Lua; while Scheme, being based around expressions, needs a more careful definition, see link above.
Otherwise yes. For instance, Scheme implementations that translate the Scheme program into portable C code (not just into bytecode interpreted by C code) cannot assume that the C compiler will translate C-level tail calls into jumps and thus take special measures to make them work correctly, from trampolines to the very confusingly named “Cheney on the M.T.A.”[1], and people will, colloquially, say those implementations do TCO too. Whether that’s correct usage... I don’t think really matters here, other than to demonstrate why the term “TCO” as encountered in the wild is a confusing one.
Cheney on the MTA is a great paper/algorithm, and I'd like to add (for the benefit of the lucky ten thousand just learning about this) that it's pun on a great old song: Charlie on the MTA ( https://www.youtube.com/watch?v=MbtkL5_f6-4 ). The joke is that in both cases it will never return, either because the subway fare is too high or because you don't want to keep the call stack around.
Because that's a description of the intended behavior, and I reason about a language as an abstraction that allows one to express an expected behavior ignoring the implementation details.
I know it's not universal: some languages in their infancy lack a formalization and are defined by their reference implentation. But a more theoretical approach has allowed languages like C to strive for years.
I still think that the language property (or requirement, or behavior as seen by within the language itself) that we're talking about in this case is "unbounded nested calls" and that the language specs doesn't (shouldn't) assume that such property will be satisfied in a specific way, e.g. switching the call to a branch, as TCO usually means.