We don't say "Happy mother's day" so we don't say 母の日、おめでとう(ございます) to other mothers, but recently, on TV, radio, ets, some people celebrate it for mothers in general. We only say お母さん、ありがとう to our own mother, at least me and I never heard people say something to other mothers like you do in English. (I think we don't say so with words but by heart.) I hope this was helpful to understand our thought.

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