What a wierd phrasing. It reads to me like it excludes the possibility of it being the same.

It's said this way because the default assumption is that a school district extends only to city or county lines. They can be larger or smaller, though.

"can be" ≠ "must be"

"can be" is used to list all possible values, which is where the confusion arises. It sounds like: ∀x, x>C v x<C.

"Might be", I think would be better.

"can" can be a synonym for "might" / "may"

(purists would argue that it can't, but common usage trumps purism)

Also, I will point out that, even from the perspective of formal logic, the original statement has "city or county". In other words there is no single fixed C - C could be a city or a country. Since counties can be larger than cities, it stands to reason that a school district could be larger than the size of a city while being equal to the size of a county. And can be smaller than the size of a county while being equal to the size of a city.

So, even assuming that the original statement is taken to have the logical meaning you've interpreted, that meaning does not technically forbid school districts from being equal to the size of a county (as long as that county is larger than some city, so that we can still make the true statement "this district is larger than a city"), nor from being equal to the size of a city (as long as that city is smaller than some county, so that we can still make the true statement "this district is smaller than a county").

MAY is the correct choice.

https://www.rfc-editor.org/rfc/rfc2119

This is not in the context of a requirement level. The definition of MAY as defined there makes no sense here.