"Living in" is often different from "reside in." It's ignorant to believe that out-of-state students who are permitted to register and vote in Ohio DON'T also vote in their home state. If Ohio is permitting out-of-state students to register and vote, then there is a problem folks - either those kids ought to be getting in-state tuition (because they are residents), or they out to be denied in-state voting (because they are not residents).
Almost every state allows college students to vote when they are on campus, even if they are from another state. In-state tuition residency laws are different than voter registration laws.
As far as the state of Ohio, and its laws concerning voter registration, living in is a synonym of residing in.