"In the year" vs "The year of"

Can an English teacher provide a technical explanation of the phrase

  1. In the year of X, Y happened
    versus
  2. The year of X, Y happened

In my view (if we are talking about the precise meaning of the phrase as opposed to the way people may talk or say such a phrase), the meaning of the phrases are

case #1) In the year of X, Y happened. X is denoting a particular year BUT X itself does not span over the whole year.
Example
In the year of my birth, my mother worked as an office clerk.
“year of my birth” denotes the year, obviously the birth itself does not span the year.

case #2) The year of X, Y happened. X is denoting something THAT SPANNED that year.
Example
The year John Smith was mayor, my friend lived in New York.
For that year, John Smith held the office of mayor for the entire year.

I ask this question, because for case #2, others have said that X’s “state” does not have to span over the whole year, and that I say, is incorrect English.

Can an English teacher provide a technical explanation of the differences between case #1 and case #2? thanks!

To begin with, one thing that should be clarified for taking a further step is: “2) The year of X, Y happened” is not 100% equivalent to the example “The year John Smith was mayor, my friend lived in New York.”

Should it be understood as: The year of John Smith’s mayorship, my friend lived in New York."?

Anyway, for the “the year of” phrase, I would think the duration depends on the context. Cf.:

i the year of John Smith’s mayorship vs. (in) the year of John Smith’s birth.[/i]

Should it be understood as: The year of John Smith’s mayorship, my friend lived in New York."?

No, it should be understood as “The year John Smith was mayor”

“The year of John Smith’s mayorship” seems to be ambiguous as to how long John Smith was mayor (at least to me), while “The year John Smith was mayor” - strongly implies that John Smith was mayor for the whole year at that point in time.

I would still think it is the qualifier not the structure, e.g., “John Smith was mayor” that determines the duration. Cf.:

“The year John Smith was mayor” vs. “The year John Smith was born”

It is the word “mayor” that implies a higher possibility of (covering) the whole year than the word “birth”, not the phrase (structure).

“The year John Smith was mayor”.
I see your point re the word “mayor”.

If somebody said to you
“The year John Smith was mayor”.

What would be your immediate understanding of the phrase, would it be
“John was mayor for a year”
or
"John was a mayor at that point in time, but not necessarily for an entire year?

“John was mayor for a year”.

And thus the discussion has now turned or would from now turn to somewhere near to semantics.