This is entirely arbitrary and knowing whether a particular place is technically part of "the city" doesn't really tell you anything about it. As you might expect, this causes a ton of unnecessary confusion.
[0] Part of Kansas City proper: https://maps.app.goo.gl/9B9rhVzAtSykLhUs5
[1] "St. Louis" but not part of St. Louis proper: https://maps.app.goo.gl/xXM7A2fQYY2Kh3vY6