AN A320 CREW; DEPARTING ATL; TURNED TO THE WRONG HEADING; REQUIRING CORRECTIVE VECTORS FROM ATC.

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ATL TWR CLRED CESSNA 210 FOR TKOF RWY 8R TO FLY INITIAL 020 DEG HDG. NEXT; ACFT Z; EMB145 CLRED FOR TKOF TO FLY 070 DEG HDG. WE WERE NEXT IN LINE; AND CLRED FOR TKOF RWY 8R TO FLY 020 DEG HDG. I AM 100% SURE OF WHAT I HEARD. THE CAPT HEARD 020 DEG HDG ALSO; AND READ IT BACK AS SUCH. RIGHT AFTER LIFTOFF; TWR ISSUED US SOME TAXI INSTRUCTIONS RELATING TO RWY 8R; TO WHICH CAPT RADIOED BACK THAT WE WERE AIRBORNE. TWR REALIZED ERROR; THEN HANDED US OFF TO DEP. CLBING THROUGH ABOUT 8500 FT MSL; DEP ASKED US TO TURN IMMEDIATELY TO A 090 DEG HDG. WE COMPLIED; AND DEP ASKED US WHAT HEADING TWR HAD ASSIGNED US. WE REPLIED 020 DEGS. HE CHKED WITH TWR; CAME BACK AND TOLD US TWR HAD US FLY 070 DEG HDG. WE SAID NO; TO PULL THE TAPES IF HE HAD TO. HE (DEP) THEN TURNED US TO A 330 DEG HDG AND HANDED US OFF TO CTR. NO TCASII TA'S OR RA'S RESULTED. SUPPLEMENTAL INFO FROM ACN 536577: ATL TWR CLRED US FOR TKOF FROM RWY 8R AND TURN TO A 020 DEG HDG AT THE MM. I TOLD DEP CTL TO PULL THE TAPES IF THEY DIDN'T BELIEVE ME. DEP CTL THEN TOLD US 'IT WAS NO BIG DEAL.' (IT'S A BIG DEAL TO ME IF I'M GOING TO HIT ANOTHER ACFT.) I FEEL THAT POOR VISIBILITY WAS A FACTOR FOR TWR AND THEY JUST GOT US OUT OF SEQUENCE OR MIXED UP FROM WHERE THEY THOUGHT WE WERE; WHICH MIGHT BE THE REASON THEY ASSIGNED US THE WRONG DEP HDG OF 020 DEGS INSTEAD OF 070 DEGS WHICH THEY SAY THEY ASSIGNED US.