A B727 PIC TAXIES ONTO RWY 31 WHEN THE TWR CTLR USES HIS CALL SIGN FOR AN ACFT CLRING THE RWY. AN ACFT ON FINAL IS SENT AROUND.

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DEPARTING LGA; HIGH WINDS NECESSITATED CHANGING DEP RWY TO RWY 31 AFTER LINE-UP FOR TKOF ON RWY 4. TWR WAS ATTEMPTING TO RUN A X-RWY OP WITH DEPS USING RWY 4 AND ARRS USING THE EXPRESSWAY VISUAL 31. ACFT WAS TAXIED WITH CLRNC DOWN TXWY B TO RWY 31. ON REACHING THE END OF TXWY B; THE ACFT WAS TURNED ONTO TXWY Z TOWARD THE HOLD LINE FOR RWY 31. THIS WAS TO FACILITATE DEP BTWN ARR ACFT. OUR ACFT WAS IN LEAD OF 3 ACFT TAXIING TO RWY 31 FOR DEP. TWR STATED THAT OUR DEST HAD INSTITUTED A GND STOP AND WE SHOULD RETURN TO LGA GND CTL. ON CALL-UP; GND DIRECTED A R TURN ON TXWY Z FOR TAXI TO AN AREA TO AWAIT RELEASE. OUR RESPONSE WAS THAT WE WERE FACING THE RWY AND UNABLE TO COMPLY. GND WAS TOLD BY US 'WE WILL HAVE TO USE THE RWY ONE WAY OR ANOTHER;' TO CLR THE TXWY/RWY ENTRANCE. GND DIRECTED A RETURN TO TWR. AN ACFT LANDED AND WAS DOWNFIELD PREPARING TO EXIT THE RWY. WE RPTED ON FREQ WITH TWR. THE RESPONSE RECEIVED WAS 'ACR X; MAKE 2 LEFT TURNS; MAKE A L AND YOUR FIRST L.' WE RESPONDED; 'ACR X; L TURN AND TAKE THE FIRST L.' FOLLOWING THIS CLRNC THE LNDG LIGHTS WERE TURNED ON AND WE TAXIED ONTO RWY 4 WITH A L TURN. SHORT FINAL WAS CLR. TWR THEN QUERIED 'ACR X; ARE YOU ON THE RWY?' THE RESPONSE; 'YES.' TWR SENT AN ACFT AROUND THAT WAS MANEUVERING FOR FINAL AND WE EXITED. NOTHING MORE WAS SAID. POSSIBLE CONTRIBUTIONS TO THIS CONFUSION; 1) CTLR USED OUR CALL SIGN FOR INSTRUCTIONS TO ACFT CLRING RWY. 2) TERMINOLOGY -- NO ONE USED TXWY OR RWY IDENTS. 3) THE PACE OF THE OP DICTATED BY XING RWY OPS AND HAZARDOUS WINDS. 4) RAPID CHANGING OF CTL (TWR/GND/TWR) RESULTS IN NOT EVERYONE HAVING THE FULL PICTURE; YET EXPECTATIONS ARE PRESENT IN ALL INVOLVED PARTIES. THIS MAY LEAD TO A DISCONNECT IN WHAT PEOPLE THINK IS HAPPENING AND REALITY.