A320 ON SHORT FINAL TO RWY 4R AT ORD IS ISSUED CONFUSING CLRNC BY ATC AND INITIATES A TURN AWAY FROM THE APCH COURSE.

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THIS IS TO INFORM YOU THAT DURING THE APCH TO RWY 4R AT ORD; CLRED TO LAND WITH INSTRUCTIONS TO EXIT THE RWY AT TXWY Q BELOW 1000 FT; WE RECEIVED THIS INQUIRY BY THE TWR; 'ACFT X; CAN YOU MAKE A L OR R TURN?' IT WAS A VERY AMBIGUOUS QUESTION AND WE SUPPOSED THAT; DUE TO THE CLOSENESS OF THE PRECEDING TFC; THEY WANTED A 360 DEG TURN TO EITHER SIDE. THE FO REPLIED; 'WE CAN MAKE IT' REFERRING TO CONTINUE THE APCH AND LNDG. THE REPLY WAS CLR BY THE TWR; 'UNABLE ACFT X;' THEN WE REPLIED THAT BY THE R SIDE WOULD BE BETTER. I INITIATED A R TURN; NOT A MISSED APCH. AT THAT TIME WE WERE AROUND 500 FT AGL. AS WE WERE PASSING THROUGH 100 DEG HDG; WE RECEIVED A REPLY FROM TWR ASKING WHAT WE WERE DOING. THE FO ANSWERED; 'A 360 DEG R TURN.' THEN TWR INSTRUCTED US TO TURN TO A HDG OF 90 DEGS AND TO CLB TO 4000 FT; A NW APCH PATTERN; AND FINALLY A LNDG WITH THE SAME ROLLOUT INSTRUCTIONS AS IN THE PREVIOUS APCH. ONCE OUT OF THE RWY; THE TWR ASKED US; 'ACFT X; DO YOU KNOW WHAT IS A R TURN?' THE FO ANSWERED; 'AFFIRMATIVE.' NO FURTHER TALKING ABOUT THIS MATTER. AS A BACKGND; DURING THE DSCNT; WE WERE VECTORED ALMOST DIRECTLY TO THE ILS RWY 4R; KEEPING US AT 8000 FT. WHEN THE DSCNT PATH WAS ABOUT 3000 FT BELOW OUR ALT; APCH CTL CLRED US TO INTERCEPT THE ILS AND TO MAINTAIN 180 KTS. UNTIL THE FINAL FIX; AS WE WERE DSNDING; I NOTICED THAT WE WERE CLOSER THAN USUAL TO THE PRECEDING TFC AND STARTED LOWERING MY SPD. AS MY EXPERIENCE SHOWS; ATC INSTRUCTIONS INFLT ARE TO BE CLR AND UNDERSTANDABLE; NOT AMBIGUOUS AS THIS ONE -- CAUSING THIS TYPE OF COM ERROR; INCREASED BY NON NATIVE ENGLISH SPEAKING PLTS.