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Kunta is a unit of local government, a municipality. Kaupunki is a city or town. You could argue that there can be severel towns (kaupunki) in one municipality or one town could be spread over several municipalities.

But kunta and kaupunki are used interchangeably in finnish and I think the one officially used is just decided by the local council.

This is a pet peeve of mine. The lack of clarity affects how people think about local politics. We should clearly define cities as continuous urban areas and let that affect more how zoning decisions are made. I believe it would reduce partial optimization.