Gulfstream Jet Captain reported Gulfstream's PlaneView database indicated the charts were current but in actuality were not; leading the flight crew to nearly fly into a TFR while on an outdated departure from PBI airport.

Narrative

Departing Runway 10L at PBI on leg #2 of the day; we were cleared via the TBIRD7 Departure. The revision info was checked during preflight prior to leg #1 and noted that the dataset was valid. During the pre-departure brief in PBI; while reviewing the departure procedure; neither crew member noticed that the chart we were reviewing was actually the TBIRD6 and not the TBIRD7. At approximately 500 feet AGL upon switching to Departure Control; ATC immediately told us turn left heading 300; climb and maintain 7;000 you're flying the TBIRD6 not the TBIRD7and about to enter the TFR. We complied immediately and nothing else was said by ATC other than cleared direct TBIRD resume own navigation. Once we were safely away from the high workload area; we reviewed the chart again and realized that our charts were actually out of date and we had the TBIRD6 [Departure] even though the chart page in PlaneView indicated the revision was up to date. The change to the departure was made 7 days prior and I believe a better system needs to be developed to get this information to pilots especially when it involves circumnavigating a TFR. There is way too much garbage in the NOTAMs and an important change like this is merely given a vague reference like 'TFR in effect check NOTAMs' rather than something specific like 'hey we changed the departure so you don't fly through the TFR.'