B737-300 CREW EXITED LNDG RWY ONTO ANOTHER RWY WITHOUT CLRNC TO TAXI ON THAT RWY.

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FLEW VISUAL APCH TO RWY 28 AT BWI. LNDG ROLLOUT EXITED ONTO RWY 33L WITH IMMEDIATE R TURN ONTO TXWY R. COMPANY ACFT WAS ON SHORT FINAL FOR RWY 33L. AS I APCHED THE INTXN OF THE 2 RWYS; I WAS SLOWING; ANTICIPATING A TURNOFF AT THE INTXN. AT THAT SAME TIME; TWR RADIOED ABOUT REPOSITIONING DUE TO TFC ON FINAL FOR RWY 33L. HE SAID SOMETHING ABOUT TXWY R1 AND I ASSUMED WRONGLY THAT HE MEANT THE R TURN OFF OF RWY 33L. HOWEVER; A SECOND LOOK AT THE COMMERCIAL CHART PAGE SHOWED TXWY R1 TO BE THE NEXT EXIT PAST THE INTXN. NO GAR WAS NECESSARY DUE TO THE SEPARATION WE HAD AND THE SHORT TIME WE WERE IN THE INTXN. PROBABLE CAUSES: 1) UNFAMILIARITY WITH SPECIFIC TXWY INTXN IN BWI. 2) ASSUMPTION OF MY PART THAT TWR WAS ASKING US TO EXPEDITE THE TURN OFF WITH PERMISSION TO USE RWY 33L FOR THE TURN ONTO TXWY R. 3) TWR'S RADIO XMISSION WAS NOT REAL CLR. PREVENTION: 1) LISTEN CLOSER TO INSTRUCTION AND IF UNSURE; TAKE THE CONSERVATIVE APCH AND ROLL TO NEXT INTXN. 2) NEVER ASSUME AN INTXN EXIT WILL BE GIVEN. 3) REVIEW WITH FO POSSIBLE TXWYS FOR EXITING THE RWY PRIOR TO LNDG.