A C650 DEPARTED CTAF SDL IFR WITHOUT AN ATC RELEASE BECAUSE THE FO MISUNDERSTOOD ATC'S DEP RELEASE.

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THE TWR HAD CLOSED FOR THE NIGHT; HOWEVER; AS WE TAXIED OUR CITATION III FOR DEP AT SDL THERE WERE STILL 4 OR 5 AIRPLANES TAKING OFF OR LNDG AT THE NOW-UNCTLED ARPT. I WANTED TO REMAIN SITUATIONALLY-AWARE OF THE TFC AT THE ARPT; SO I REMAINED ON CTAF AND HAD MY COPLT GO OFF ON THE OTHER RADIO AND CALL PHX APCH CTL FOR AN IFR DEP RELEASE. MY COPLT CAME BACK AND SAID WE WERE 'CLRED TO GO' BEHIND A LNDG HAWKER JET. AFTER THE HAWKER LANDED WE DEPARTED BUT WHEN WE CONTACTED DEP CTL AND RPTED AIRBORNE CLBING TO 5000 FT THE CTLR WAS SURPRISED AND ASKED IF WE HAD DEPARTED VFR. IT OCCURRED TO ME THAT A DEP RELEASE SHOULD HAVE INCLUDED A TIME AND VOID TIME. I SUSPECT WHAT THE APCH CTLR TOLD MY COPLT WAS TO 'EXPECT TO DEPART' BEHIND THE HAWKER; WHICH IS NOT A DEP RELEASE. LATER IN THE FLT WE DISCUSSED MY CONCERN AND MY COPLT WASN'T ABLE TO TELL ME WHAT THE CTLR'S WORDS WERE; SO THAT MADE ME EVEN MORE SUSPICIOUS. FORTUNATELY; CONDITIONS WERE VFR. IN THE FUTURE I'LL MONITOR THE OTHER RADIO WITH THE COPLT.