MD80 CREW BEGAN A CLB TO FL310 WHEN THEY WERE CLRED TO HDG 310 DEGS.

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DEV FROM CLRNC ALT. LEVEL AT 17000 FT MSL; ENRTE TO ELIOT INTXN WE RECEIVED A RADIO CALL FROM CTR TO TURN TO '310.' FO READ BACK THE HDG IN HIS SOFT SPOKEN MANNER. HOWEVER I THOUGHT THE CTLR GAVE US A CLB CLRNC TO FL310. I REPEATED FL310 TO THE FO AND CHANGED THE ALT MYSELF. I THOUGHT FOR SURE HE HAD POINTED AT THE '310' IN THE WINDOW I HAD SET. I STARTED A SLOW CLB INITIALLY AND AT 17800 FT MSL THE CTLR CORRECTED US TO DSND TO 17000 FT MSL. THERE WERE NO TFC CONFLICTS ACCORDING TO THE CTLR. IMC CONDITIONS AND A BUSY SCRATCHY RADIO CONTRIBUTED TO THE CONFUSION. SUPPLEMENTAL INFO FROM ACN 631173: I RECEIVED A CLRNC FROM ATC TO 'TURN R HDG 310 VECTORS FOR CLB.' I THEN LOOKED AT MY SID PLATE TO SEE IF ANYTHING ELSE APPLIED TO OUR DEP. AS I LOOKED BACK TO THE INST PANEL I NOTICED WE WERE CLBING AND '310' WAS SET IN THE ALT WINDOW AND WE DID NOT TURN FROM OUR ORIGINAL HDG. AS I WAS ASKING THE CAPT IF HE SET THAT ALT IN THE WINDOW; THINKING I MISSED SOMETHING HERE; ATC CALLED AND ASKED OUR ALT; I SAID 17600 FT. SHE SAID TO GO BACK TO 17000 FT; WHICH WE DID. SHE THEN ASKED WHAT ALT WE WERE CLBING TO AND I SAID FL310. THEN SHE SAID THAT WAS A HDG OF 310 DEGS NOT AN ALT AND SENT US DIRECTLY TO ELIOT. THE CTLR SAID WE DID NOT CAUSE ANY PROBS.