After doing absolutely zero research on the topic, I have come up with both a list and some firm rules regarding the distinction between suburb and exurb in Minnesota and specifically the Minneapolis / St. Paul / Twin Cities area.
Is there open land / farm land between two cities? If so, the more distant of the two from the core city (in this case Minneapolis or St. Paul) is an exurb. Connections are what make suburbs. Endless stretches of houses, strip malls and unwalkable streets with no farm land separating said cities make suburbs.
Burnsville and Lakeville are suburbs. Elko New Market is an exurb. Shakopee and Prior Lake are suburbs, as is their neighbor Savage. Jordan and Belle Plaine are exurbs. Drive down 169 and you’ll see why Jordan and Belle Plaine are exurbs.
Chaska is a suburb. Its neighbor, Carver, is a suburb as well because it is connected to Chaska. Waconia, though, is an exurb.
To the north you have Forest Lake. Forest Lake is an exurb. And then there’s North Branch which might as well be part of Duluth or at least Hinckley. I’m kidding North Branch, I love your little two-bit outlet mall.
Argue all you want but these are the rules of what separates suburbs and exurbs along with some damn sold examples.