NON ADHERENCE TO AN 'IMMEDIATE' OR 'START DSCNT NOW' TYPE CLRNC.

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I WAS PIC -- OPERATING RADIO (NOT FLYING). FO FLYING. THE FOLLOWING IS THE SEQUENCE OF RADIO XMISSIONS AND ACFT PERFORMANCE THAT OCCURRED. ATL APCH: 'CLRED R TURN DIRECT LGC; MAINTAIN FL220.' READBACK: 'R TURN DIRECT LGC; MAINTAIN FL220.' FO INITIATED R TURN DIRECT LGC. APCH: 'CLRED TO CROSS TIROE AT 14000 FT/250 KTS; ATL ALTIMETER 30.03. DOWN TO FL180 NOW; EXPECT A TURN BACK TO LGC SOON.' READBACK: 'OK; CLRED TO CROSS TIROE AT 14000 FT/250 KTS; ALTIMETER 30.03; SAY AGAIN THE REST.' APCH: 'DISREGARD THE REST.' READBACK: 'ROGER; TIROE AT 14000 FT/250 KTS. AT THIS POINT WE ASSUMED THE DSCNT WAS AT PLT DISCRETION TO CROSS TIROE AT 14000 FT/250 KTS. THE CONFUSION CAME WHEN WE WERE TOLD TO 'EXPECT A TURN BACK TO LGC SOON.' SINCE WE WERE ALREADY CLRED DIRECT LGC; WE THOUGHT THE CTLR WAS PROBABLY TALKING ABOUT ANOTHER AIRPLANE. WHEN I ASKED THE CTLR TO 'SAY AGAIN THE REST' ABOUT THE FL180 HE REPLIED 'DISREGARD THE REST.' WE TOOK THAT TO MEAN WE WERE TO DISREGARD THE 'DSND TO FL180; NOW.' A FEW MIN LATER APCH CALLED: 'I NEED YOU DOWN THROUGH FL180; START DOWN NOW.' READBACK: 'YES SIR; YOU TOLD ME TO DISREGARD THE REST;' 'WE ARE IN THE DSCNT NOW' OR 'WE ARE OUT OF FL220.' APCH: 'CALL THROUGH FL200.' READBACK: 'ROGER; THROUGH 20100 FT AND NOW THROUGH FL200.' AS WE WERE GOING THROUGH FL200 WE RECEIVED A TCASII TA. -- A YELLOW DIAMOND AT 12 O'CLOCK ON THE RADAR SCOPE SHOWING AN ACFT CLBING 900 FT ABOVE US. I FEEL THE CONFUSION BEGAN WHEN WE WERE TOLD TO EXPECT A CLRNC 'SOON;' A CLRNC WE HAD ALREADY RECEIVED; THUS MAKING US FEEL THE CLRNC WAS PROBABLY INTENDED FOR ANOTHER ACFT. THE CTLR WAS VERY BUSY GIVING NUMEROUS ACFT DELAYING VECTORS; ALT; AND AIRSPD CHANGES. I BELIEVE THE DENSITY OF TFC IN ATL DURING THIS 'PEAK' PERIOD OF TIME WAS A CONTRIBUTING FACTOR. THE SYS WAS SATURATED. I THINK THE CTLR SHOULD HAVE RESTATED THE 'DSND NOW TO FL180.' AFTER HE TOLD ME TO 'DISREGARD THE REST.' I SHOULD HAVE BEEN MORE INQUISITIVE ABOUT A CLRNC I THOUGHT WAS PROBABLY FOR SOMEONE ELSE.