B757 FLT CREW LNDG FLL EXPRESSED CONCERN FOR COMPLETING A VISUAL APCH WHEN ATC ISSUED A GPS APCH CLRNC.

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ACCORDING TO THE FLL ATIS; THE WX WAS SCATTERED CLOUDS AT 800 FT; BROKEN AT 2500 FT; VISIBILITY 10 MI; TEMP 20 DEGS C (68 DEGS F) WIND 340 DEGS AT 9 KTS. THE NORMAL RWY USED BY ACR'S IS RWY 9L/27R. RWY 9R/27L IS TOO SHORT FOR ACR'S AND IS USED BY GA ACFT ONLY. RWY 9L/27R WAS CLOSED FOR RESURFACING; A PROCESS WHICH WOULD TAKE ABOUT 2 WKS. RWY 13/31 WAS THE ACTIVE RWY DUE TO THE CLOSURE OF RWY 9L. RWY 13/31 IS 6000 FT LONG; AND NORMALLY NOT USED BY ACR'S DUE TO ITS RELATIVELY SHORT LENGTH AND BECAUSE OF NOISE ABATEMENT CONCERNS. THERE IS A PUBLISHED LOC APCH TO RWY 13; WHICH IS THE PREFERRED RWY WHEN RWY 9L IS NOT AVAILABLE. WE FLEW DOWNWIND AT 4000 FT; W OF THE ARPT. ABEAM THE ARPT; MIA APCH CTL TOLD US TO EXPECT A VISUAL APCH; AND ASKED IF WE HAD THE ARPT IN SIGHT AT OUR 9 O'CLOCK POS; 3 MI. I TOLD APCH CTL THAT THERE WAS A BROKEN LAYER OF CLOUDS BELOW US THAT WAS BLOCKING OUR VIEW OF FT LAUDERDALE; EXCEPT FOR OCCASIONAL SIGHTINGS BTWN THE CLOUDS. APCH TOLD US TO CONTINUE DOWNWIND HDG 130 DEGS; AND THAT THEY WOULD VECTOR US ONTO APPROX A 10 MI FINAL APCH. SINCE ACR'S RARELY USE RWY 31; THERE WERE NO COMMERCIAL APCH PLATES FOR THAT RWY IN OUR BOOK BAG. HOWEVER; THE FMS DID HAVE AN 'RNAV 31' APCH IN THE COMPUTER. TO ENHANCE SITUATIONAL AWARENESS; I SELECTED THE RNAV 31 FMS APCH AND ACTIVATED IT AS A BACK-UP TO OUR VISUAL APCH. I ALSO TUNED AND IDENTED THE LOC FOR RWY 13; WHICH WAS OPERATING; DESPITE THE FACT THAT RWY 31 WAS IN USE; NOT RWY 13. THE LOC; ALTHOUGH GIVING A BACK COURSE PRESENTATION; WAS STILL USEFUL FOR SITUATIONAL AWARENESS. THROUGHOUT OUR DSNDING BASE LEG; AND DURING THE FIRST FEW HUNDRED FT OF DSCNT ON FINAL APCH THE ARPT WAS NOT VISIBLE; DUE TO THE BROKEN LAYER OF CLOUDS. AFTER WE DSNDED UNDERNEATH THE CLOUDS AT 2500 FT; I TOLD ATC THAT WE WERE NOW BELOW THE CLOUDS. MY INTENTION WAS THAT ATC UNDERSTOOD THAT WE COULD NOW CONTINUE TO FLL ON A VISUAL APCH. HOWEVER; ATC CLRED US FOR A 'GPS APCH' TO RWY 31. I ACKNOWLEDGED BY RESPONDING 'ACR X; ROGER; CLRED FOR THE APCH.' WE COMPLETED A NORMAL VISUAL APCH AND TOUCHDOWN; USING THE FMS RNAV 31 PRESENTATION AND BACKCOURSE LOC FOR SITUATIONAL AWARENESS. FLT OPS WAS CONCERNED ABOUT THE LEGALITY OF RESPONDING 'CLRED FOR THE APCH' TO ATC WHEN THEY CLRED US FOR A 'GPS APCH' INSTEAD OF SPECIFICALLY STATING 'NEGATIVE; WE DON'T HAVE APCH CHARTS FOR A GPS APCH; BUT WE CAN DO A VISUAL APCH.' I TOLD FLT OPS THAT I HAD STATED THAT WE WERE 'BELOW THE CLOUDS;' MEANING THAT WERE CAPABLE OF PERFORMING A VISUAL APCH. HOWEVER; I REALIZE THAT TECHNICALLY; WE WERE PROBABLY CLRED FOR A 'GPS APCH' BY ATC; AND THAT I SHOULD HAVE BEEN MORE SPECIFIC IN MAKING ATC AWARE THAT WE WERE EXECUTING A VISUAL APCH; SINCE WE DIDN'T HAVE A COMMERCIAL APCH CHART FOR A GPS APCH. THE LESSON LEARNED IS TO BE MORE SPECIFIC WHEN COMMUNICATING WITH ATC; FOR BOTH POTENTIAL SAFETY OF FLT REASONS AND FOR COMPLYING WITH TECHNICAL LEGALITIES.