WRONG ALT APCH CREATES A POTENTIAL CONFLICT FOR THE FLC OF A BE400 SW OF JAX; FL.

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FLT ORIGINATED FROM SGJ TO JAX. INITIAL CLRNC WAS TO CLB TO 2000 FT; HDG 310 DEGS; WHICH WAS COMPLIED WITH. FINAL ALT CLRED TO WAS 5000 FT. WHEN I HAD WHAT I THOUGHT WAS JAX IN SIGHT; I TOLD THE APCH CTLR 'ARPT IN SIGHT.' THE ARPT THAT I WAS LOOKING AT; WHICH FROM MY POS HAD THE CORRECT RWY ALIGNMENT; WAS NOT JAX; BUT WHITE HOUSER FIELD. WE WERE GIVEN A DSCNT TO 3000 FT AND INFORMED OF TFC BELOW US AT 2000 FT. WE WERE CLRED FOR A VISUAL APCH TO RWY 7 AT JAX. WE THEN STARTED A L TURN AND DSNDED FROM 3000 FT TO 2800 FT WITH TFC BELOW IN VISUAL CONTACT. I WAS ASKED BY THE CTLR WHAT ARPT I HAD IN SIGHT. BEFORE ANSWERING; THE CTLR CAME BACK WITH A VECTOR OF 020 DEGS AND ALT OF 2000 FT; FOLLOWED BY ADDITIONAL VECTORS TO A VISUAL APCH TO RWY 7 AT JAX. UPON LNDG AND CONTACTING GND; I WAS ASKED TO CALL THE CTLR SUPVR. HE SAID LOST SEPARATION HAD OCCURRED AND THOUGHT IT WOULD BE CONSIDERED A PLTDEV. I TOLD HIM I WAS VERY SORRY THE SIT HAD HAPPENED. ALSO; I TOLD HIM OF THE WRONG ARPT IN SIGHT INITIALLY; VERIFYING JAX ARPT; SHORTLY AFTER VISUAL APCH CLRNC RECEIVED; VISUAL APCH CLRNC TO RWY 7 AND PREVIOUSLY CALLED TFC IN SIGHT WITH VISUAL SEPARATION MAINTAINED WITH NO INDICATION FROM CTLR OF OTHER ACFT CLBING. CORRECTIVE ACTION I SHOULD TAKE IN THE FUTURE WOULD BE TO NEVER CALL ARPT IN SIGHT UNTIL ABSOLUTELY VERIFIED WITH ALL MEANS AVAILABLE.