FLC OF AN FK10 FAILED TO FOLLOW ATC INSTRUCTIONS WHEN THEY FLEW A HDG FROM A DIFFERENT FIX THAN THAT INTENDED; OR GIVEN; BY ATC. FURTHERMORE; THE CTLR DID NOT HEAR THE WRONG FIX WHEN THE FO READ BACK THE CLRNC. THE FLC THOUGHT THAT THEIR FMS WAS NOT RIGHT FOR NOT INCLUDING THE STAR FIX INTENDED BY ATC. HOWEVER; REVIEW OF STARS INDICATE THAT THE FIX IS NOT INCLUDED FOR THE IAD ARPT; ONLY THE DCA; WHICH WAS THE ARPT AT WHICH RPTR LANDED.

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AT APPROX XX00Z FLT WAS ON DULLES APCH (FREQ 119.85) AND GIVEN A 185 DEG HDG FROM AML. THE FO READ BACK '185 DEG HDG OUT OF AML.' AT THAT TIME A DISCONTINUITY WAS INDICATED ON THE FMS F-PLAN PAGE AT THE LAST FIX ON THE STAR. THE CAPT DIALED IN 185 DEGS ON THE EFIS PANEL AND PULLED THE HDG KNOB THUS SELECT 185 DEGS. SHORTLY THEREAFTER (1 MIN); DULLES ATC SAID CLRED DIRECT SHAKI. THE FO STATED WE WERE ON A 185 DEG HDG FROM AML. ATC SAID; 'NO; THE 185 DEG HDG WAS TO BE FROM SHAKI; NOT ARMEL. I DON'T KNOW WHAT YOU READ BACK BUT THE HDG IS 185 DEGS FROM SHAKI; FLY HDG 090 DEGS.' THE FO STATED HE HAD READ BACK 185 DEGS FROM ARMEL. (I DO NOT BELIEVE THAT WAS WHAT THE CTLR SAID.) THERE WAS SOME ADDITIONAL DISCUSSION BTWN THE CAPT AND ATC IN REGARDS TO THE DISCREPANCY IN WAYPOINTS AND FIX. CAPT STATED THAT SHAKI IS NOT IN OUR FMS DATABASE FOR THE STAR AND THAT WE WOULD FORWARD THIS TO THE COMPANY FOR CORRECTION AND CHANGE. THE CAPT ASKED ATC IF THE DEV HAD CAUSED ANY PROBS AND ATC STATED NONE. FLT COMPLETED APCH AND LNDG AT DCA. AS A FOOTNOTE; ATC INDICATED THAT OTHER ACRS HAD SIMILAR PROBS WITH FMS DATABASES AND AREA STARS IN SPECIFIC DULLES DEPS. CTLR (ATC) SHOULD HAVE CAUGHT THE INCORRECT READBACK (IF IN FACT IT WAS INCORRECT) AND CORRECTED THE VOICE COM.