We've been having a real issue with these signs popping up everywhere in OK. My local bank put one up and I went to talk to the manager about it. He "assured me" that the intent of the sign wasn't to keep out people with a concealed permit. It was intended to keep out the newly legal in OK, the open carry types. I told him I still didn't want to have to see that sign every time I walked into the bank.
In OK, the sign doesn't have "the force of law." If they figure out you are armed, they can ask you to leave. The problem is that these signs are essentially creating a new space: the no legal open carry space. Despite the fact that we have seen zero problems in OK with open carry.
So yeah, concealed means concealed and I would walk in right past the sign in OK. But it WOULD mean I couldn't open carry in there. I couldn't be arrested but I could be asked to leave almost immediately.