CONFUSION AND POTENTIAL TFC CONFLICT DEPARTING ZZZ WHEN THE DEP BEING FLOWN IS NOT THE ONE EXPECTED WHEN AN ACR DC9 IS HANDED OFF TO CTR.

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DURING TAXI OUT; WE INFORMED GND CTL THAT WE NEEDED TO DEPART RWY XX BECAUSE OF WT RESTR. GND CLRED US TO TAXI TO RWY XX. GND CTL SAID TO EXPECT RWY XX WITH A NW DEP. WE STATED THAT THE DEP WE SHOWED FOR RWY XX WAS THE RWY XX COMPANY PUBLISHED 2 DEP AND GND CTL SAID THAT WAS THE 'ONE.' TWR CLRED US FOR TKOF ON RWY XX AND THEN IMMEDIATELY HANDED US OFF TO CTR FOR DEP CTL. WE MADE OUR REQUIRED TURN ON THE RWY XX COMPANY PUBLISHED 2 DEP AND CONTACTED CTR. CTR ASKED US WHICH RWY WE HAD DEPARTED AND WHICH DEP WE WERE FLYING. WE RESPONDED WITH RWY XX AND THE RWY XX COMPANY PUBLISHED 2 DEP. CTR TOLD US TO EXPEDITE OUR CLB THROUGH 7500 FT AND TURN TO A 130 DEG HDG FOR TFC. WE COMPLIED WITH CTR'S INSTRUCTIONS THEN ASKED WHY WAS THERE A CONFLICT. CTR STATED ZZZ HAD TOLD HIM WE WERE FLYING A DIFFERENT DEP. WE RESPONDED THAT WE CONFIRMED THE RWY XX COMPANY PUBLISHED 2 DEP WITH GND CTL BEFORE TKOF. I THINK ZZZ GND CTL EITHER DID NOT UNDERSTAND THE RWY XX COMPANY PUBLISHED 2 DEP OR FAILED TO COORDINATE WITH CTR. THERE MAY HAVE ALSO BEEN CONFUSION WITH THE TERMINOLOGY USED AND THE COMPANY RWY XX COMPANY PUBLISHED 2 DEP. THIS IS A COMPANY PUBLISHED DEP FOR RWY XX AND THE ONLY DEP WE HAVE PUBLISHED FOR RWY XX. IN RETROSPECT; I THINK THE CTLR MAY HAVE WANTED US TO DEPART TO THE NW (MAGNETIC DIRECTION) AFTER DEP BUT THERE IS NO PUBLISHED DEP FOR RWY XX TO SHOW THIS AND NO HDG WAS GIVEN BY GND CTL OR THE TWR WHEN WE WERE CLRED FOR TKOF. WE THOUGHT IT WAS CLRLY UNDERSTOOD THAT WE INTENDED TO FLY THE RWY XX COMPANY PUBLISHED 2 DEP SINCE THIS IS THE DEP WE DISCUSSED AND CONFIRMED WITH GND CTL DURING TAXI.