Suppose I went to the supermarket three times. Is my third trip considered my "second time returning there" or my "third time returning there?" Thanks. (I know this question sounds silly, but English is my second language...)
You've gone to the store at a few times, t1, t2, t3, t4,...
t1 is the first time, t2 is the second time etc.
Did you return to the store at time t1? No, the meaning of 'return' is that you've been there at least once and you've visited again.
At time t2, can you say you've returned? Yes. Is t2 the first time you've returned? If you haven't visited the store anytime between t1 and t2, then yes.
On t3, how many times have you visited the store? Three. How many times have you returned to the store. Two times. So at time t3 you're retuning to the store the second time.
It is not a silly question. I think these expression are ambiguous, and different people (or different contexts) may interpret them inconsistently.
If you say
I returned for the second [or third, etc.] time.
the meaning is ambiguous. Is this the second time in total or the second revisit after the inital visit. As such, the construction should be avoided unless there is other context that explains exactly how many visits have preceeded the one you are now describing.
Perhaps a better construction might be
My initial visit was delightful. But after I returned two more times, the appeal wore off.
I go to the store to buy cheese.
I return to the store to buy cheese.
I return to the store once again. I have returned to the store twice. I've returned to buy cheese three times.
Case number 3 is not "returning a third time", it is returning with the intention to "buy cheese a third time".
It's ambiguous to express simply by counting returns. Many other languages have similar problems with this concept. Bib's second construction implies that the word "more" is useful: "I came to buy cheese. This is the second time I've come back for more." (Or ",,,the third time I've come for it.")