A DA900 FO FAILED TO CANCEL THEIR FLT PLAN AFTER THE CAPT ASKED THE FO TO CANCEL IT.

Narrative

I WAS THE CAPT ON AN IFR FLT LNDG AT GAI. UPON ADVISING POTOMAC APCH WE HAD THE ARPT (GAI AN UNCTLED ARPT) IN SIGHT WE WERE CLRED FOR A VISUAL APCH AND THEN ASKED IF WE WANTED TO CANCEL THE IFR AND MAINTAIN THE CURRENT SQUAWK; OR CALL ON THE GND TO CANCEL OUR IFR FLT PLAN. I TOLD THE FO TO TELL THE CTLR THAT WE WOULD CANCEL THE IFR FLT PLAN ON THE GND AFTER LNDG. UPON CLRING THE RWY I TOLD THE FO THAT I WOULD MONITOR THE ARPT UNICOM FREQ AND ASKED HIM TO CANCEL THE IFR FLT PLAN WITH POTOMAC APCH. WHILE TAXIING IN I HEARD THE FO READING BACK OUR OUTBOUND CLRNC AND 'ASSUMED' THAT HE HAD NOTIFIED POTOMAC APCH OF THE CANCELLATION SINCE HE WAS READING BACK THE OUTBOUND CLRNC. WHILE WE WERE REFUELING; A SINGLE ENG ACFT TAXIED UP AND THE PLT ADVISED ME THAT HE WAS TOLD BY POTOMAC APCH THAT THEY HAD NOT RECEIVED OUR IFR CANCELLATION. I IMMEDIATELY INQUIRED WITH THE FO ABOUT THE CANCELLATION. HE SAID THAT HE TOLD THE CTLR THAT WE WERE ON THE GND AT GAI AND WERE LOOKING FOR AN IFR CLRNC TO MMU. I SPECIFICALLY ASKED HIM IF HE TOLD THE CTLR THAT HE WAS CANCELING THE IFR FLT PLAN? AFTER SOME HESITATION FROM THE FO; I CALLED POTOMAC APCH ON MY CELL PHONE AND IDENTED MYSELF AS THE CAPT TO VERIFY THEY HAD RECEIVED OUR CANCELLATION. I WAS ADVISED WE WERE NOT CANCELLED AND THEY WERE GETTING READY TO SEND OUT A SEARCH CREW AND FILE A RPT ON US. I TOLD THE CTLR THAT IT WAS MY FAULT AND THAT WE ROUTINELY OPERATE AT THAT ARPT AND I AM FAMILIAR WITH THE IFR CLRNC AND CANCELLATION PROCS. I ADVISED THE CTLR THAT I WOULD DISCUSS WITH MY FO THE IMPORTANCE OF PROPER PHRASEOLOGY AND TERMINOLOGY.