In the U.S., the census department defines the metro areas based on a number of factors (like one factor is the number of commuters). …m.wikipedia.org/…/Metropolitan_statistical_area

There’s also a larger combined statistical area that often involves multiple major cities that are close enough to form an economic region. For instance, DC and Baltimore basically share suburbs and are connected by public transportation: …wikipedia.org/…/Washington–Baltimore_combined_st…

I believe greater is only used colloquially here but the UK’s Office of National Statistics uses “Greater” in a formal way: …m.wikipedia.org/…/Greater_London_Built-up_Area …wikipedia.org/…/Greater_Manchester_Built-up_Area

I assume that’s why it’s part of North American vernacular.