In a shipping module's settings, if you select --None-- from the Shipping Zone pulldown, then the module will not apply any address-restrictions.
If you wish to do any restricting, you must define a zone so that it appears in that list, and then select it.
Zones are defined in Admin->Locations/Taxes->Zone Definitions.
If you wish to define a zone which applies to all 48 states, you create the zone (perhaps call it "Continental US"), and then click on the Details button and then add all applicable country+state combinations. ie: select United States for the country, and then one of the states. Then click Add, and repeat again and again for all the states you wish to include in that zone.
Then when you edit the shipping module you'll be able to select the "continental U.S." module from the Shipping Zone pulldown, so that that module will be available only to addresses whose country/state combination fall inside the list of defined country/state combinations you put into that zone.
That's all entirely separate from your "Ohio" zone definition used solely for taxes.
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