A COMMUTER FLC ACCEPTS THE ALT CLRNC FOR ANOTHER ACR AHEAD OF THEM WHILE ON RADAR VECTORING TO FINAL AT CAK; OH.

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WE WERE ON APCH INTO CAK. TALKING WITH CAK APCH HE CLRED US DOWN TO 4000 FT FROM 5000 FT AND TOLD US TO EXPECT VISUAL APCH TO RWY 1 AND WE READ THE CLRNC BACK TO HIM. WE THEN HEARD CLRNC DOWN TO 3000 FT; WHICH WE ALSO READ BACK TO HIM. (I WAS THE PF; MY FO WAS WORKING THE RADIOS.) AT THE TIME THERE WAS AN ACR Y ON THE FREQ WHO WAS AHEAD OF US ON THE VISUAL TO RWY 1. A MIN OR SO LATER; ATC ASKED US WHAT ALT WE WERE AT. WE RESPONDED 3000 FT. HE TOLD US WE WERE CLRED TO 4000 FT AND TO EXPECT THE VISUAL TO RWY 1; THAT THE 3000 FT CLRNC WAS FOR ACR Y. I RESPONDED THAT YES WE WERE CLRED TO 4000 FT AND TO EXPECT RWY 1; BUT THEN WE HEARD CLRED DOWN TO 3000 FT; WHICH WE READ BACK TO HIM ALSO. I ASKED HIM IF HE WANTED US BACK UP TO 4000 FT; WHICH HE SAID JUST STAY AT 3000 FT. I THOUGHT AS FAR AS RADIO COM WAS CONCERNED WE FOLLOWED PROPER PROC. MY FO AND I BOTH HEARD THE SAME CLRNCS. I ALSO HEARD MY FO'S RESPONSES ON THE RADIO. IF WE HAD GOTTEN THE WRONG CLRNC BY READING IT BACK WE SHOULD HAVE BEEN CORRECTED AND WEREN'T. FACTORS THAT MIGHT HAVE CONTRIBUTED TO THE POSSIBILITY THAT WE READ BACK OTHER ACR'S CLRNC WAS THE FLT TIME FROM CLE-CAK. IT IS A 10-15 MIN FLT WHICH REQUIRES A LOT OF WORK FOR THE PNF: READING CHKLISTS; CALLING COMPANY AFTER DEP AND IN- RANGE; GETTING ATIS AND WRITING IT DOWN; LOOKING UP LNDG SPDS; ETC. THIS WAS ALSO OUR FOURTH TRIP OF THE DAY. THE OCCURRENCE HAPPENED AT XI40 AND WE RPTED TO WORK AT XA20 ON THE THIRD DAY OF A 3 DAY TRIP.