If a state recognizes another's conceal carry permits, what happens if the second state passes a Constitutional Carry law?

Could you still carry in the first state if you were visiting? Would your driver's license or other ID "become" your carry permit? Sorry if this is a stupid question, the recent passage of the constitutional carry bill through the MO house has me curious. Thanks! via /r/CCW http://ift.tt/1Ti4H0H