at/on retirement.

Pretty much.

You'll note the use of "his". That suggests, "on his retirement", that the gift was given at a function in his honour on the day of his retirement; maybe only a speech or two in the lunch break, but a social event nevertheless.

Thank you.

But you say at/on are the same, then if the money given 'at retirement' does not happen at a function on the day of retirement, when will it be?

-Your pension plan provides a cash lump sum at retirement.
The pension plan provides a cash lump sum which is payable on or after the date of the employee's retirement. "At retirement" denotes a stage in his employment.

-a gift from the company on his retirement
He received a gift from the company, which presumably was physically handed to him (presented to him) at a social function in his honour.

But note, as I said before, the two phrases are practically the same.

Thank you, but do you think there are other phrases using 'at' the same way?

I think 'on' is the same as 'on arrival', etc.

Yes, it is used in this way to denote stages: at birth, at puberty, at onset of old age, at death.

Suddenly I see bright light! Thank you.

Good man.