MLG CREW HAD A RWY INCURSION WHILE TAXIING TO RWY 24 AT TEB.

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AFTER REQUESTING TAXI CLRNC AT THE FBO AT TEB; I HEARD GND CTL SAY 'TAXI TO RWY 24.' WE COULD SEE 6 OR 7 ACFT ON THE PAD NEXT TO RWY 24. THE FO SAID 'THAT MEANS WE CAN CROSS ALL RWYS.' AFTER VISUALLY CLRING THE APCH AREA TO RWY 19; I PROCEEDED TO CROSS RWY 19. ALMOST OFF OF RWY 19; GND CTL XMITTED TO EXPEDITE XING RWY 19. THEN GND CTL SAID 'YOU WERE SUPPOSED TO HOLD SHORT OF RWY 19.' THE FO DID NOT READ BACK HOLD SHORT OF RWY 19 BECAUSE THAT WAS NOT STATED BY GND. MAYBE GND SAID TAXI TO RWY 19; I DO NOT KNOW. THEN GND CTL SAID 'POSSIBLE PLT INFRACTION.' I DO NOT KNOW WHO WAS RIGHT OR WRONG. SUPPLEMENTAL INFO FROM ACN 546435: UPON CALL-UP TO TAXI; WAS GIVEN 'TAXI TO....' WAS NOT GIVEN A HOLD SHORT OF ANY RWY. CREW MADE A WRONG ASSUMPTION THAT WE COULD TAXI TO ACTIVE RWY. POSSIBLE RWY INCURSION. TWR/GND ALSO SEEMED CONFUSED AS TO CLRNC. CREW SUSPECTED CTLR TRAINING IN PROGRESS. CORRECTIVE ACTION INCLUDED CREW DISCUSSING WHAT EVENTS AND INFO COULD HAVE LED US TO BELIEVE WE WERE CLRED TO ACTIVE. NEITHER CREW MEMBER HEARD A HOLD SHORT CLRNC. BOTH CREW MEMBERS RESOLVE TO HAVE UTMOST DILIGENCE IN TAXI CLRNC AND ASK FOR FURTHER INSTRUCTIONS IF UNSURE.