MD80 FLT CREW MISUNDERSTANDS DEPS IN USE AT DFW.

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I WAS SERVING AS A CHK AIRMAN IN THE R SEAT GIVING CAPT RE-QUALIFICATION FLTS AFTER A MEDICAL LEAVE OF ABSENCE. WE HAD LOADED AND BRIEFED THE DARTZ 2 RNAV DEP IN THE FGMS AND WERE SET TO FLY IT. WE WERE NOT TOLD TO CHK IN WITH 'Q' OR RPT OUR FIRST WAYPOINT TO TWR SO WHEN WE HEARD SOMEONE WE THOUGHT WAS THE TWR CTLR SAY 'WE ARE NOT DOING RNAV DEPS TODAY' ON TWR FREQ WE THOUGHT WE WERE DOING RADAR VECTORS ON DEP. WE TOOK OFF AND FLEW RWY HDG WHILE WAITING TO BE SWITCHED TO DEP CTL. AFTER TKOF; TWR DID NOT CALL US TO SWITCH TO DEP; SO I TRIED CALLING THEM TO ASK IF THEY WANTED US TO SWITCH. THE FREQ WAS BUSY SO WE SWITCHED OURSELVES AND CHKED IN. I ASKED DEP IF THEY WANTED US TO CONTINUE TO FLY A HDG. THEY SAID THEY THOUGHT WE WERE SUPPOSED TO BE FLYING AN RNAV DEP SO WE ENGAGED THE NAV AND FLEW THE DARTZ DEP SINCE WE WERE RIGHT ON COURSE. I DON'T KNOW WHO SAID THEY WERE NOT CONDUCTING RNAV DEPS BUT WE SHOULD HAVE CONFIRMED THAT CLRNC PRIOR TO TKOF. WE WERE IN CLR DAY VMC AND WELL CLR OF OTHER TFC ON THE DARTZ NAV TRACK SO AS SOON AS COM WAS ESTABLISHED WITH DEP WE ENGAGED NAV AND COMPLIED WITH THE DARTZ DEP.