FLC OF LR55 FAILED TO FOLLOW THE SID BY TURNING TOO EARLY THE WRONG WAY DUE TO REFING THE WRONG SID.

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WE WERE GETTING READY TO DEPART DAL-FXE. CLRNC ISSUED THE DALLAS 4 DEP IN WHICH I PULLED THE PLATE TO REVIEW WITH THE CAPT. BEFORE ENG START; THE CAPT BRIEFLY REVIEWED THE PLATE; THEN WHILE TAXIING OUT; THE CAPT ACCIDENTALLY STARTED REVIEWING THE OPPOSITE SIDE OF THE DEP PLATE WHICH IS THE BUCHMAN 2 DEP; WHICH IS SIMILAR IN APPEARANCE. WHILE NEITHER I NOR MY CAPT NOTICED THIS; HE CONTINUED TO REVIEW AND STATED THAT WE WERE DEPARTING RWY 31R AND HE LOOKED ON THE DEP PLATE AND SAW WHAT HE THOUGHT WAS RWY 31R BUT WAS ACTUALLY RWY 13R AND READ THE DEP INSTRUCTIONS. THESE ARE TO TURN R TO HDG 160 DEGS AFTER TKOF. THE CORRECT DEP INSTRUCTIONS ARE TO MAINTAIN RWY HDG TO 5000 FT. AFTER TKOF; WE STARTED OUR TURN TO 160 DEGS BUT OUT OF 2000 FT THE TWR TOLD US TO TURN BACK TO HDG 290 DEGS. AT THAT POINT I KNEW SOMETHING WAS WRONG AND TOLD THE CAPT TO VERIFY THE DEP. HE REALIZED HE WAS LOOKING AT THE WRONG PLATE. WE TURNED TO 290 DEGS AND THE REST OF THE FLT WAS UNEVENTFUL. THE DEPS ARE VERY SIMILAR IN NATURE. GOOD CRM WOULD ELIMINATE CONFUSION IN THE DEPS OUT OF DALLAS LOVE.