SOME CONFUSION ABOUT AN ACR'S FLT NUMBER LEADS THE FLT CREW TO BELIEVE THAT ATC HAS THEM MIXED UP WITH ANOTHER ACR'S IDENTITY DURING APCH; LNDG AND TAXI AT BUR; CA

Narrative

FO'S FIRST TIME IN BUR. CAPT'S MOST RECENT BUR EXPERIENCE WAS YEARS BEFORE. INBOUND TO BUR; SOCAL APCH AND TWR THOUGHT THAT WE WERE ANOTHER ACR Y B737; DUE THEIR TFC CALLS TO US ABOUT 'COMPANY TFC' THAT WAS THE OTHER ACR Y B737. AFTER LNDG; TWR TOLD US TO TURN R AT THE END OF RWY 8 AND FOLLOW (WRONG) ACFT Y COMPANY B737. AS WE WERE TAXIING; WE HEARD TWR GIVE INSTRUCTIONS TO OUR COMPANY FLT XX TO STOP ABEAM THE TWR. WE WERE FLT XY AND EVEN THOUGH WE RECOGNIZED THIS TO BE A SIMILAR CALL SIGN; IT WAS STILL A DIFFERENT CALL SIGN. WE THEN SWITCHED TO GND FREQ AND CHKED IN; WHEREUPON THE GND CTLR TOLD US TO 'TAXI TO THE GATE.' PASSING ABEAM THE TWR; THE GND CTLR ABRUPTLY TOLD US TO HOLD POS. THEN WE NOTICED 2 ACFT TAKING OFF FROM RWY 15. AFTER THE ACFT TOOK OFF; WE WERE THEN INSTRUCTED TO CONTINUE TAXIING TO THE GATE. ALTHOUGH IT WAS NEVER CONFIRMED; WE THINK THAT GND CTL WANTED US TO HOLD SHORT OF THE RWY 15 HOLD SHORT LINE; EVEN THOUGH THEY USED THE WRONG CALL SIGN; AND ON THE WRONG FREQ TO TELL US. FURTHERMORE; THIS INSTRUCTION CONFLICTED WITH THE GND CTLR'S INSTRUCTION TO CONTINUE TAXIING TO THE GATE.