ACR ISSUED TFC; SIGHTED; BUT THERE WERE 2 ACFT IN SAME AREA. RECEIVED TCASII RA.

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BRADLEY APCH CTL ADVISED TFC AT 11 O'CLOCK; A COMMUTER. I WAS UNFAMILIAR WITH THE DESCRIPTION BUT ASSUMED IT WAS THE CARRIER IDENT. THERE WAS TFC AT 11 O'CLOCK AND I CALLED IT. PROBLEM WAS THERE WERE 2 ACFT AT 11 O'CLOCK. I IDENTED/SAW THE LARGER OF THE 2 (WHICH LATER WAS IDENTED AS ACR-MLG). WHEN I ACKNOWLEDGED WHAT I ASSUMED WAS THE INTENDED TFC; I TOOK UP VISUAL SEPARATION ON IT; AND THE ATC CTLR RELINQUISHED HIS RESPONSIBILITY FOR INTENDED TFC. NEXT CAME TCASII TA THEN RA TO 'CLB CLB'. TCASII RA WAS FOLLOWED. TWIN ENG TURBOPROP PASSED OFF L WING LESS THAN 1000 FT. THE TCASII TA/RA SEEMED TO BE CORRECT. ATC APCH WAS ADVISED OF OUR DEV AND WHY. PHONE CONVERSATIONS WERE HELD WITH ATC AND LATER; THE TWR. IN MY ESTIMATION; THERE WERE 2 CONTRIBUTING FACTORS TO THIS UNNECESSARY TCASII ALERT. FIRST; THE XMISSION/TA FROM APCH CTL COULD HAVE BEEN MORE SPECIFIC (IE; PAINT A PICTURE -- '2 TARGETS AT 11 O'CLOCK; ACR-MLG HDG SE AT 4000 FT AND A TWIN ENG COMMUTER AT 5000 FT HDG SW; RPT THE TWIN ENG COMMUTER IN SIGHT'). SECONDLY; BECAUSE THE ADVISORY WAS NOT AS CLR (TO ME) AS IT COULD HAVE BEEN; I CALLED A VISUAL SIGHTING ON THE ACFT I COULD SEE AT 11 O'CLOCK. UNFORTUNATELY IT WAS AN ADDITIONAL ACFT AND NOT THE INTENDED ONE.