An honorary aunt is a close friend of the parents who is called an aunt, though not related by blood. For example, if you have a friend who has a baby, you may be called an aunt (or uncle) by the child and parents even though you're not related.
Your Aunt is your children's Great Aunt.
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I call my grandma's aunt, Great Aunt. Maybe that's what you call her, but she is of course your great-great-aunt.
He received honorary degrees from Harvard, Yale, University of St. Andrews (Scotland; Doctor of Laws), and Oxford (for science).
He would call your aunt his great aunt. In informal situations, great aunts are sometimes called, simply aunt.