A TWR GND CTLR AND A VEHICLE DRIVER BECAME CONFUSED AS TO THE CLRNC GIVEN REGARDING A 'FIELD CHK.'

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AT LNS WE HAVE A PROC FOR RWY FIELD CHKS BY THE ARPT AUTH. A 'W FIELD CHK' FOR RWYS 26/31 AND AN 'E FIELD CHK' FOR RWYS 8/13. THIS PARTICULAR NIGHT WE WERE USING RWY S 26/13 DUE TO A STRONG S WIND. AN ARPT VEHICLE CALLED FOR A FIELD CHK FROM THE ARPT AUTH LOCATED NEAR THE APCH END OF RWY 8. MY REPLY; 'ARPT VEHICLE DRIVER; GND; W FIELD CHK; HOLD SHORT RWY 31.' THE VEHICLE RESPONDED; 'ARPT VEHICLE DRIVER; ROGER; HOLD SHORT RWY 31.' WE BOTH ASSUMED SOMETHING DIFFERENT...ASSUMED. AT THIS POINT I SHOULD HAVE RESTATED 'W OP' BUT I DID NOT. NEXT; A PLT NEEDED PROGRESSIVE TAXI INSTRUCTIONS OUT TO RWY 13. ARPT VEHICLE DRIVER WAS BEHIND THE TAXIING SMA ON THE RAMP WITH A DIM YELLOW FLASHER ON HIS ROOF. AS I TAXIED THE SMA; I LOST SIGHT OF THE VEHICLE; SO I STARTED BACKTRACKING FROM THE APCH END OF RWY 31 TO THE RAMP HE LEFT; SEARCHING FOR HIM. NEXT; TWR GOT AN LTT COMMUTER INBOUND 8 SE FOR RWY 26. THE LCL CTLR SCANNED RWY 26 TO GIVE THE COMMUTER LTT HIS LNDG CLRNC AND WE BOTH WERE SURPRISED AT THE SAME TIME. IN FRONT OF US; DRIVING E ON RWY 8 WAS ARPT VEHICLE DRIVER. WE GOT THE VEHICLE OFF THE RWY AND THERE WAS NO LOSS OF SEPARATION. ON THE PHONE; WE DISCUSSED WHAT HAPPENED SO IT WOULD NOT HAPPEN AGAIN. ARPT VEHICLE DRIVER SAID HE ASSUMED I WANTED AN 'E FIELD CHK LIKE LAST NIGHT; SO HE FOLLOWED THE SMA OFF THE RAMP; WENT ON RWY 8 TO HOLD SHORT OF RWY 31; THEN CROSSED RWY 31 TO CONTINUE WITH THE CHK. I THEN TOLD HIM I ASSUMED HE UNDERSTOOD A W FIELD CHK; SO I WAS LOOKING FOR HIM FROM RWY 31; BACK TO THE RAMP. ALSO; WE AGREED; ALL THE VEHICLES FLASHING LIGHTS SHOULD BE ON; 4-WAYS; LIGHT BARS; AND THE YELLOW LIGHTS. ALSO; THE COMMUTER LTT HAD REQUESTED THE RWY EDGE LIGHTS TURNED UP FULL INTENSITY SO HE COULD SEE IT BETTER. THE RWY LIGHTS WERE BRIGHTER THAN THE VEHICLE'S WHICH MADE IT HARDER TO SEE HIM.