Is ojiisan an idiomatic word choice for a chronologically gifted man, akin to obaasan for elderly women? For example, when giving your seat to them on the train.
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おじいさん means both a grandfather and an elderly man. When written in kanji, it is written as お祖父さん when it means grandfather, and written as お爺さん when it means elderly man. The same applies to おばあさん (お祖母さん/お婆さん).
It is natural to call an elderly man おじいさん. However, I have heard that some people do not like the use of おじいさん and おばあさん which mean elderly man and woman, and that in particular they do not like to be called that way. I guess that the reason for this is that calling a person おじいさん or おばあさん may imply that the most relevant attribute of the person is his/her age. Although I do not find it reasonable, I may hesitate to call someone who I do not know at all おじいさん or おばあさん to avoid unnecessary conflict.
By the way, similarly to おじいさん and おばあさん, おじさん can mean an uncle or a middle-aged man, and written as 伯父さん (elder brother of parent), 叔父さん (younger brother of parent), or 小父さん (middle-aged man, but not commonly written in kanji). The same applies to おばさん (伯母さん, 叔母さん, 小母さん).
Note that you can also call middle-aged woman 奥さん and middle-aged man 旦那さん, ご主人さん. (What I mean by middle-aged is 35~55+). Not really used by young people, rather between middle-aged people or from staff to customer; さん becomes さま then.
As well, you can call young people (15~30) おにいさん/おねえさん even if they are younger than you. In Kansai, we call staff this way too (I believe it's not common in Tokyo area).