I have a friend whose family I also know. Her mother likes me, and addresses me as her "(my ethnicity) daughter", or herself as my "(her ethnicity) mother" as a form of endearment. I live in a Western, English-speaking country where I am an ethnic minority, and she is part of the ethnic majority.
I don't have a problem with her being friendly, and even pointing out my minority status continuously doesn't bother me as much as the fact that she calls herself my mother. I have a very close relationship with my own mother, who is the only mother I need, and feel quite uncomfortable that my friend's mother is almost putting herself on equal footing with my mother despite not having 'earned it'.
At the same time, I understand it is her way of expressing affection, and would like to tell her that calling me her daughter, or herself as my mother makes me uncomfortable without coming across as rude. This has also gone on for many years and I have not previously indicated that it was unwelcome (although I have also never encouraged it or used the terms myself).
Edits to include comments:
- The mentioned friend is her daughter, and they have a good relationship, so it is not the case that I am 'a daughter she always wanted', but she just has a normal level of affection for me.
- I have always called her by her first name. She also doesn't exclusively refer to me as 'daughter', more often it is by my first name, but the term 'daughter' does surface once in a while.
- I would be happy with any non-familial endearment term, and some familial or quasi-familial terms (e.g. aunty), where there is no restriction on the number of these that you can have (as opposed to godmother, where there is typically just one).