A B737 FLT CREW AND CYYZ TWR HAVE A DIFFERENCE OF OPINION ABOUT WHAT THE TAXI CLRNC WAS.

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WE CONTACTED GND CTL AFTER CLRING A LNDG ON RWY 5. WE HEARD OUR INSTRUCTIONS TO BE 'CROSS RWY 15L; HOLD SHORT TXWY T.' THE FO READ BACK 'CROSS 15L; HOLD SHORT TXWY T.' AFTER XING RWY 15L; WE TURNED R ON TXWY B PROCEEDING TOWARD TXWY T TO HOLD SHORT. THE GND CTLR INFORMED US AS WE BEGAN OUR TAXI ON TXWY B THAT OUR CLRNC HAD BEEN TO TAXI ON RWY 15L. I RESPONDED THAT WE UNDERSTOOD AND READ BACK OUR CLRNC TO BE CROSS THE RWY. HIS RESPONSE WAS 'NO.' HE THEN ADDED THAT HE WOULD CLR THE EQUIP OUT OF OUR WAY AND TO CONTINUE TAXIING ON TXWY B TO HOLD SHORT OF TXWY T. THIS WAS SOMEWHAT CONFUSING TO US AS WE WERE THE ONLY ACFT IN SIGHT ANYWHERE ON THE FIELD AND THE ONLY EQUIP WAS APPROX 1/2 MI AWAY SNOWPLOWING AN INTERIOR RAMP. WE CONTINUED TAXI WITHOUT FURTHER CONFUSION TO THE GATE. I AM NOT REALLY SURE IN THE FUTURE WHAT CAN BE DONE TO IMPROVE OR ELIMINATE THIS TYPE OF CONFUSION. HAD ANY OF THE RELEVANT TXWYS BEEN NOTAMED CLOSED; HAD THERE BEEN ANY OTHER ACFT IN SIGHT; HAD THERE BEEN ANY OTHER EQUIP IN SIGHT; THEN WE CERTAINLY WOULD HAVE QUESTIONED OUR CLRNC. AT NO TIME WAS THERE LOSS OF SEPARATION OR TAXI CONFLICT WITH GND EQUIP. THERE WAS; HOWEVER; DEFINITE COM ERROR BTWN US AND THE GND CTLR.