BE36 PLT AND ANOTHER ACFT WERE BOTH CLRED TO LAND ON RWY 20L AT PDK.

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ARRIVING IFR FROM THE NE; I PICKED UP THE ARPT 5 MI OUT AND WAS CLRED FOR THE VISUAL APCH RWY 20L. I POSITIVELY IDENTED RWY 20L; THE LONG RWY CLOSEST TO MY POS. I DISTINCTLY REMEMBER SAYING 'CLRED FOR THE VISUAL RWY 20L' TO REPEAT THE CLRNC. I THEN RPTED L BASE RWY 23L BY MISTAKE. IT JUST CAME OUT WRONG. I WAS CORRECTED BY THE CTLR AND 'CLRED TO LAND RWY 20L.' I THEN DISTINCTLY REPEATED 'CLRED TO LAND; RWY 20' SO HE WOULD KNOW I CORRECTED IT. THINGS CONTINUED WITH 'BUSINESS AS USUAL' AS THE CTLR POINTED OUT MY POS TO ANOTHER ACFT TWICE WHILE I WAS ON FINAL FOR RWY 20L. AT AN ALT OF 200 FT; I HEARD A PLT ON THE GND WAITING FOR TKOF KEY THE MIKE AND SAY 'THERE ARE 2 PLANES THAT ARE GOING TO LAND ON EACH OTHER.' THEN I HEARD THE TWR CTLR TELL ME TO 'GO AROUND IMMEDIATELY;' WHICH I DID. HE ASKED ME TO TURN R AND THE OTHER ACFT TO TURN L. I THEN HEARD THE CTLR SAY SOMETHING TO THE OTHER ACFT; AND HE SEEMED ANNOYED WITH THE OTHER PLT. HE THEN ASKED ME TO ENTER A R DOWNWIND FOR RWY 20R AND I COMPLIED. HE ASKED ME 'DO YOU SEE RWY 20R?' AND I ANSWERED 'YES I DO.' HE THEN SAID 'CLRED TO LAND RWY 20R...THAT'S WHERE WE WANTED YOU THE FIRST TIME.' THAT STATEMENT WORRIED ME BECAUSE I HAD NO RECOLLECTION OF HEARING THE CTLR SAY ANYTHING ABOUT RWY 20R AT ANY TIME PRIOR TO THAT STATEMENT. IT WAS 'BUSINESS AS USUAL' WITH THE CTLR POINTING OUT MY POS TO THE OTHER ACFT ALL THE WAY DOWN FINAL FOR RWY 20L. I DO NOT BELIEVE THAT IF I HAD IT TO DO OVER AGAIN THAT I WOULD HAVE OR COULD HAVE DONE ANYTHING DIFFERENTLY TO HAVE PREVENTED THIS NEAR MISS. THE CTLR SAID NOTHING MORE TO ME.