B717-200 FLT CREW MISIDENTS CONFLICTING TFC AND LANDS AT HNL WITHOUT CLRNC.

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HNL APCH CTL WAS GIVING US RADAR VECTORS TO A VISUAL APCH TO RWY 8L. APCH CTL TOLD US TO MAINTAIN 2000 FT AND TO EXPECT LOWER WHEN WE WERE CLR OF TFC ON APCH TO RWY 4L. THE FO RESPONDED THAT HE HAD THAT TFC IN SIGHT AND I NOTED THAT THERE WAS A LIGHT ACFT AT OUR 1-2 O'CLOCK LOW POS THAT APPEARED TO BE HEADED IN THE DIRECTION OF THE 4L/4R RWYS. I ADVISED HNL APCH CTL THAT WE HAD THE TFC IN SIGHT. HNL APCH CTL THEN DIRECTED US TO 'MAINTAIN VISUAL SEPARATION WITH THE TFC; KEEP HIM OFF TO YOUR R; CLRED VISUAL APCH TO RWY 8L.' THE PF BEGAN HIS DSCNT OUT OF 2000 FT AND AT APPROX 1800 FT MSL THE TCASII ANNUNCIATED 'TFC; TFC' THEN 'REDUCE DSCNT; REDUCE DSCNT.' THE TCASII TARGET BOX WAS RED. THE PF LEVELED OFF AT 1800 FT MSL AND I SAW A SINGLE ENG CESSNA TYPE ACFT AT OUR 11 O'CLOCK LOW POS AT ABOUT 1/2 MI HORIZ DISTANCE. I THINK THAT WE PASSED DIRECTLY OVER THE TOP OF THE CESSNA WITH 800 FT SEPARATION. I WAS SURPRISED TO SEE THAT ACFT AS I THOUGHT THAT WE HAD ALREADY PASSED THE ADVISED TFC AND WERE CLR OF HIM. I WAS NOT AWARE THAT THERE WERE 2 ACFT ON SEPARATE APCHS TO THE RWYS 4L AND 4R AND I DON'T RECALL HNL APCH CTL ADVISING US OF A SECOND ACFT IN OUR VICINITY. WE WERE BOTH IN A STATE OF SURPRISE AND AS WE CONFIGURED THE ACFT FOR LNDG OUR MINDS WERE BOTH PREOCCUPIED WITH THE THOUGHT OF HOW CLOSE WE HAD JUST COME TO A MIDAIR COLLISION AND THINKING ABOUT HOW WE COULD HAVE AVOIDED IT. IN THE LNDG FLARE; ABOUT 5 SECONDS BEFORE TOUCHDOWN; THE PF ASKED ME IF WE WERE ON TWR FREQ. I REPLIED 'YES;' BUT IN THE NEXT MOMENT I HAD THE REALIZATION THAT THE RADIO WAS STILL ON APCH CTL'S FREQ AND NOT THE TWR FREQ; AND AT THAT MOMENT WE TOUCHED DOWN. I SWITCHED OVER TO TWR'S FREQ AND ADVISED THEM THAT WE WERE CLRING AT TXWY G. THEY 'ROGERED' AND CLRED US TO TAXI TO RAMP ON THEIR FREQ. AS I REFLECT UPON THE EVENTS THE CHAIN OF ERRORS BECOMES APPARENT. WHEN APCH CTL ISSUED THE TA FOR THE ACFT ON APCH TO RWY 4L WE MISIDENTED THAT TFC. WE ASSUMED THAT IT WAS THE ACFT THAT WE OBSERVED CLOSEST TO US AND I CALLED IT 'IN SIGHT' WITHOUT VERIFYING ACFT TYPE AND POS. PERHAPS IF I HAD VERIFIED THE ACFT TYPE AND ITS POS RELATIVE TO US; APCH CTL MIGHT HAVE BEEN ALERTED TO THE FACT THAT WE DID NOT HAVE THE CORRECT ACFT IN SIGHT; AND MAYBE THE 'ERROR CHAIN' MIGHT HAVE BEEN BROKEN RIGHT THEN. I AM NOT 100% CERTAIN; BUT I DON'T RECALL APCH CTL ADVISING US THAT THERE WERE 2 ACFT ON SEPARATE APCHS TO RWYS 4L AND 4R. IF WE HAD BEEN AWARE OF THAT FACT WE WOULD HAVE BEEN LOOKING FOR THE SECOND CONFLICTING ACFT BEFORE WE BEGAN OUR DSCNT FROM 2000 FT. THE APCH CTLR MUST HAVE BEEN SPEECHLESS AS SHE WATCHED 2 TARGETS CROSS PATHS WITH ONLY 800 FT OF VERT SEPARATION AND WE NEVER RECEIVED THE USUAL INSTRUCTIONS TO CONTACT THE TWR FOR LNDG. MYSELF; BEING PREOCCUPIED WITH WHAT HAD JUST HAPPENED; I NEGLECTED TO COMPLETE THE BEFORE LNDG CHKLIST AND LEFT OUT THE 'LNDG CLRNC' CHALLENGE TO THE PF. A WRONG ASSUMPTION; THAT I HAD THE CORRECT ACFT IN SIGHT; STARTED (OR POSSIBLY BECAME A LINK IN) A CHAIN OF ERRORS WHICH LED TO A LOSS OF SITUATIONAL AWARENESS (AN UNCOMPLETED LNDG CHKLIST AND LNDG WITHOUT A CLRNC). I HAVE SINCE BECOME VERY CAREFUL ABOUT IDENTING AND VERIFYING CONFLICTING AIR TFC BEFORE I WILL ADVISE A CTLR THAT I HAVE THE TARGET IN SIGHT. I NOW VERIFY TARGETS BY REPEATING TO AIR TFC CTLRS THE TYPE OF ACFT; AZIMUTH AND DISTANCE WHEN CONFIRMING THAT I HAVE ANOTHER ACFT IN SIGHT. I ALSO MAKE IT A POINT TO HAVE THE BEFORE LNDG CHKLIST COMPLETED BY 1000 FT AGL.