[samatman]

There's a real ambiguity, but it isn't in the examples you gave.

It's the case of saying "next Tuesday" on a Thursday, and meaning that no Tuesdays will pass before the date in question, versus saying "next Thursday" on a Tuesday, where a Thursday will happen before the date.

That's because on Thursday, "this Tuesday" has already happened. But sometimes people will be thinking of "Tuesday after next" when they say "next Tuesday" on a Thursday, because they mean "the Tuesday after the coming Tuesday" and not "the Tuesday of next week".

[tpmoney]

Both cases are still ambiguous because even though “this” Tuesday has already passed on Thursday, no one gets confused when you say “I’m having a cook out this Tuesday, want to come?” because the future tense of the sentence automatically excludes the Tuesday in the current week which has already passed.

Since “next Tuesday” also puts the sentence context into the future, the ambiguity exists around whether it means “Tuesday in 5 days” or “Tuesday in 12 days”

If no such ambiguity existed, we wouldn’t need common phrases like “this coming Tuesday” which clarifies the speaker is talking about the “next Tuesday with no other Tuesday’s in between”

Amusingly I don’t think there’s much ambiguity around “the Tuesday after next” as a phrase even though it should be equally ambiguous, but I’ve never heard that phrase to mean “3 Tuesdays from now”