Ohio doesn't require "a specific type of sign." There are no requirements other than that there is a sign that prohibits weapons, or concealed carry. The sign could be verbal, pictorial, could use any sort of language. It's not specified.
Thus, it's not a really a "grey area." If you can tell it's posted, then it's prohibited and the prohibition carries the force of law.
"A constitutional guarantee subject to future judges’ assessments of its usefulness is no constitutional guarantee at all." -- Justice Antonin Scalia, DISTRICT OF COLUMBIA ET AL. v. HELLER, June 26, 2008