AN ACR EMB120 MISUNDERSTOOD TWR 'POS AND HOLD' INSTRUCTIONS AND READ BACK THEIR CALL SIGN AND INTO POS. ANOTHER ACR; WHO THE CLRNC HAD BEEN FOR; ADVISED RPTR THAT THE CLRNC WASN'T FOR THEM. TWR CTLR STOPPED THE OTHER ACR AND CLRED RPTR FOR TKOF SINCE THEY WERE OVER THE HOLD LINE.

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WE WERE #1 FOR RWY 34R AT TXWY H1 IN FRONT OF SEVERAL ACFT AWAITING DEP. WE WERE CONDUCTING THE BEFORE TKOF CHKLIST TO THE LINE WHEN A CLRNC FOR POS HOLD RWY 34R WAS ISSUED. THE FIRST PORTION OF THE CLRNC WAS ILLEGIBLE BECAUSE OF THE CHKLIST BEING PERFORMED; ALL THAT WAS HEARD FOR SURE WAS 'INTO POS AND HOLD; RWY 34R.' THE CAPT QUERIED THE FO IF THE CLRNC ISSUED WAS FOR OUR FLT. THE FO RESPONDED TO ATC BY ANNOUNCING SPECIFICALLY 'POS AND HOLD RWY 34R; ACR A.' WITH NO CONTRARY RESPONSE FROM ATC WE PROGRESSED WITH THE REMAINDER OF THE CHKLIST AND STARTED A SLOW TAXI ONTO THE RWY. THE CLRNC ISSUED WAS FOR AN ACR B ACFT; POS AND HOLD FROM TXWY H2. THE ACR B FLT OBSERVING THE LIGHTS AND STROBES OF OUR ACFT MADE A COM DIRECTED TO US THAT THE POS AND HOLD CLRNC WAS NOT FOR THE ACR A ACFT AT TXWY H1. WE IMMEDIATELY STOPPED THE ACFT OVER THE HOLD SHORT LINE BUT PRIOR TO THE ACTUAL RWY. THE ATC CTLR OBSERVED THE SAME; THEN ISSUED A CLRNC FOR ACR A TO CONTINUE INTO POS AND HOLD AND TOLD THE ACR B FLT TO HOLD SHORT RWY 34R. UPON THE DEP HDOF ATC ADVISED ACR A TO CONTACT THE SLC CTL TWR UPON ARR AT THE DEST ARPT. THE CAPT UPON CALLING SLC TWR; AND EXPLAINING THE ABOVE SIT WAS TOLD BY THE TWR SUPVR THAT NO ACTION WOULD BE INSTIGATED BY THE SLC TWR AND THAT THE SIT WAS CLOSED. THE TWR SUPVR INDICATED THAT THE WORKING LCL CTLR HAD BEEN DEBRIEFED AND COUNSELED THAT IN A HIGH TFC SIT; IT WOULD BE ADVISABLE TO NOTIFY THE ACFT THAT WAS WAITING #1 FOR DEP FOR THE RWY; THAT AN OUT OF SEQUENCE DEP FROM AN INTXN WOULD BE FORTHCOMING.