B737-800 FLT CREW HAS A TRACK HDG DEV DURING DEP FROM LGA ON THE LGA 9 DEP.

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AT 17000 FT; ON ASSIGNED HDG I THOUGHT THE CTLR TOLD ME TO FLY HDG 180 DEGS DIRECT WHITE INTXN. I THOUGHT THAT'S WHAT I READ BACK TO HER; 180 DEGS DIRECT WHITE. WE WERE ALSO AT 270 KTS ASSIGNED. CAPT WAS TAKING CARE OF AN ISSUE IN THE BACK AND DID NOT HEAR THESE CALLS. I DIALED IN 180 WHICH WAS A GOOD VECTOR IN THAT IT TOOK US RIGHT TO WHITE. LNAV ENGAGED; HERE WE GO. THEN ATC SAYS WHEN ESTABLISHED DIRECT TO COLTS NECK RESUME NORMAL SPD. I'M LOOKING AT MY PFD SHOWING ME DIRECT WHITE THEN CYN. COLTS NECK IS NOT ON OUR FLT PLAN SO I'M THINKING CYN IS COLTS NECK; AND I ASK HER DID SHE MEAN THAT AFTER WHITE AND THEN ESTABLISHED TOWARD COLTS NECK NORMAL SPD. SHE SAID (I BELIEVE) NO I TOLD YOU TO GO DIRECT TO COLTS NECK. CAPT GETS OFF THE PHONE AND I TELL HIM WE'RE GOING DIRECT TO COLTS NECK. HE SAID THAT'S NOT ON OUR PLAN. I ASK ATC FOR AN IDENT FOR COLTS NECK AND THEN I SEE IT ON THE LOWER PART OF THE SID. IT'S COL. ABOUT THEN SHE GIVES US A HDG OF 160 DEGS AND THEN A CLRNC DIRECT TO WHITE. I MISUNDERSTOOD WHAT SHE SAID; WAS UNFAMILIAR WITH COL; WAS EXPECTING DIRECT WHITE (ESPECIALLY AFTER HER VECTOR OF 180 DEGS TOOK US RIGHT TO WHITE). CAPT WAS OFF THE AIR DEALING WITH A FLT ATTENDANT THAT WAS TELLING HIM THAT SHE THOUGHT THE SLIDE WAS HANGING OUT OF THE ACFT. SUPPLEMENTAL INFO FROM ACN 696931: THE FO APPEARED CONFUSED ABOUT A CLRNC AND HAD SELECTED A DIRECT TO CYN IN THE FMS WITHOUT CONSULTING ME; THINKING IT WAS COL; THE FIX HE WAS CLRED TO.