KANSAS CITY, Kan. and Mo. — Two cities, two states, one name, separated by a Patrick Mahomes shovel pass.

Welcome to Kansas City, Kansas. Wait. (Walks 14 steps.) Kansas City, Missouri!

Standing in front of Papa Vic’s The Jigger, a sports bar in Kansas City, Mo., the view across the aptly named State Line Road is one of a glassy skybridge, bearing the words, “The University of Kansas Hospital.” It’s about the only sign at this part of the border that makes it clear you’re not in Missouri anymore. You’re in Kansas City, Kan.

Those who live in either city generally excuse outsiders who confuse them, but not so much when that outsider is President Trump, and certainly not when making the mistake in front of 72 million followers on Twitter after a hard-won Super Bowl.

“It doesn’t bother me that much; it bothers me that he’s ignorant,” Sara Ohadi-Hamadani, a 33-year-old medical student at the University of Kansas, said of Mr. Trump’s now infamous gaffe, in which he congratulated the “Great State of Kansas” for the Kansas City Chiefs’ Super Bowl victory against the San Francisco 49ers.