Two different bills. The Brady Bill was background checks, originally with a waiting period possible but only for handguns, transitioning to the instant check and including all firearms. (I bought a 1911A1 just after the bill passed and before it went into effect, then bought a Maverick 12 ga with 18.5 inch barrel right before the "instant check" went into effect. (Would have bought something like an AR-15, but couldn't afford it just then, got what I could).
The Assault Weapons ban (which Kasich did indeed vote for) was part of Bill's Crime, aka "Violent Crime Control and Law Enforcement Act of 1994" (H.R.3355 103rd Congress), complete with funding for 10,000 cops, which never appeared, and for Midnight Basketball for inner city Yutes. The Brady bill (H.R.1025 103rd Congress) passed first. Kasich voted *against* the Brady bill).
thank you for the correction.