"Then the question in Ohio becomes what if you carry a screwdrive with the intent to use it as a weapon? "

The 'intent' portion of those laws, from my understanding, is to help citizens not get in trouble for carrying a knife and getting stopped for having a busted tail light. In many locations, historically, if you are stopped for any reason you can be charged with concealed weapon violations etc by just carrying a pocket knife and having a police officer in a bad mood.

The 'intent' portion basically says that in order to get in trouble for carrying a legal knife (ie under 5.5" in blade length in Texas) you have to be in the commission of a crime. The government basically has to prove you intend to use the knife as a weapon in order for you to get in trouble for it.

If you are carrying a knife while breaking into a store you could very well also be charged with intent to use a deadly weapon.