N90 CLRS A320 DIRECT; AS UNDERSTOOD BY FLT CREW AS 'DREMS' (PRONOUNCED BY N90 AS 'DREAMS') ONLY TO BE CHALLENGED FOR NOT PROCEEDING DIRECT 'GRENE' INTXN.

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VECTORED OFF THE MILTON ARR TO THE E (E OF DREMS INTXN) ON A HDG. WE WERE THEN TOLD TO TURN L TO 040 DEGS DIRECT TO DREMS (WE HEARD IT PRONOUNCED AS 'DREAMS'). WE INITIATED A DIRECT TO DREMS. A SHORT WHILE LATER; ATC ASKED US OUR HDG (WE WERE IN THE TURN TOWARDS DREMS) AND WE SAID WE'RE TURNING L TO GO DIRECT TO DREMS. ATC TOLD US TURN R TO A HDG OF 080 DEGS AND GO DIRECT TO GRENE INTXN. GRENE INTXN IS ON THE ILS RWY 4 APCH PLATE TO LGA AND DREMS IS ON THE MILTON ARR INTO LGA. WE NOW REALIZED THAT THE INITIAL CLRNC WHICH WE HEARD AS 'DIRECT TO DREMS AND ACKNOWLEDGED AS SUCH WAS ACTUALLY 'GO DIRECT TO GRENE.' WE PROCEEDED DIRECT TO GRENE INTXN. THERE WAS NO TFC CONFLICT THAT WE WERE ADVISED OF BY ATC OR TCASII. THE PRONUNCIATION BY THE CTLR OF 'DREMS' AND 'GRENE' SOUNDED SO SIMILAR TO EACH OTHER; WE FELT THAT CONTRIBUTED TO THE CONFUSION. AT THAT POINT IN THE FLT WE WERE STILL ON THE ARR AND SO THOUGHT THAT 'DREMS' WAS WHAT ATC INTENDED FOR US TO GO TO. MAYBE ONE OF THESE INTXNS SHOULD BE RENAMED TO PREVENT CONFUSION OF THIS SAME THING IN THE FUTURE.