FLT CREW OF B737 CONFUSE RAMP CTL INSTRUCTION FOR ATCT GND CTL CLRNC AND CROSS RWY WITHOUT CLRNC.

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DURING PUSHBACK FROM GATE AT CLT; WE WERE REQUIRED TO CALL CLRNC DELIVERY FOR OUR RELEASE TIME. CALLED RAMP CTL AND WERE TOLD TO FOLLOW COMPANY ACFT FOR RWY 36R. UPON XING RWY 5/23; WE WERE TOLD TO CONTACT CLT GND CTL. WE THEN REALIZED WE HAD CONTINUED TAXI AND CROSSED AN INACTIVE RWY WITHOUT CLRNC FROM GND. THE CLRNC WE THOUGHT WE HAD TO TAXI TO RWY 36R MAY HAVE ACTUALLY CAME FROM RAMP CTL. RAMP CTLRS (IN AN ATTEMPT TO BE LIKE AN ATC CTLR) OFTEN USE TERMINOLOGY SIMILAR TO ATC CTLR. THIS TECHNIQUE BLURS THE DISTINCTION BTWN RAMP AND ATC GND CTL. FOR INSTANCE; RAMP USUALLY TELLS ACFT TO GO TO THE 'SPOT' AND CALL GND; BUT THIS TIME THEY TOLD US TO 'FOLLOW THE COMPANY ACFT TO RWY 36R.' OTHER FACTORS CONTRIBUTING TO THIS ERROR WERE THE DUTY DAY OF NEARLY 13 HRS; FLT TIME OF 7 HRS 30 MINS; ONLY GETTING 4 HRS SLEEP THE NIGHT BEFORE DUE TO LONG DAYS SPENT IN MOVING. THIS WAS AN HONEST MISTAKE BOTH THE CAPT AND MYSELF MAKE. WE WERE BOTH STUNNED AS TO HOW THIS COULD HAVE POSSIBLY HAPPENED AND NEITHER ONE CAUGHT THE MISTAKE. WE BOTH CONCUR THAT WE BOTH HEARD A TAXI CLRNC AND I BELIEVE I RESPONDED TO ONE; BUT I MAY HAVE DONE SO ON CLRNC DELIVERY FREQ OR RAMP CTL. AND THE TAXI CLRNC WE HEARD MAY HAVE BEEN FOR THE COMPANY ACFT WE WERE FOLLOWING. NEITHER OF US EVER REALIZED ANYTHING WAS AMISS UNTIL WE HAD CROSSED THE RWY AND WERE TOLD BY RAMP CTL TO CALL GND. WE VIEW THIS VERY SERIOUSLY AND ACT PROFESSIONALLY WHILE AT WORK. THANKFULLY; RWY 5/23 WAS NOT IN USE NOR DID CLT TWR HAVE TO USE IT FOR AN EMER ACFT.