POTENTIAL CONFLICT BTWN AN APCHING LR45 AND ANOTHER ACFT ON FINAL FOR RWY 19 AT TEB.

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I WAS IN THE PROCESS OF FLYING ACFT X INTO TEB. THE WX AT THE TIME WAS VMC. OUR ARR INTO THE ARPT CONSISTED OF VECTORS FOR THE VOR A. WE WERE CLRED FOR THE APCH AND CONTACTED TWR WHEN WE GOT THE HDOF FROM APCH CTL. THE FREQ WAS EXTREMELY CONGESTED AND WHEN WE WERE EVENTUALLY ABLE TO CONTACT TWR; WE WERE INSTRUCTED TO 'CROSS MIDFIELD AT 1500 FT; MAKE L TFC FOR RWY 19.' DURING THE CIRCLING PROCESS; WE HEARD SEVERAL CALLS TO ACFT Y; ANOTHER COMPANY ACFT; WHICH WAS NOT UNUSUAL. AS WE WERE MANEUVERING FOR RWY 19; WE HEARD ANOTHER CALL FOR ACFT Y TO 'GO AROUND.' AT THIS POINT; I QUERIED THE CTLR AS TO WHETHER OR NOT HE MEANT TO ADDRESS US; ACFT X. HE REPLIED IN THE AFFIRMATIVE; SO WE WENT AROUND TO BE FOLLOWED BY AN UNEVENTFUL LNDG. IN RETROSPECT; AFTER WE WERE TOLD TO MAKE L TFC FOR RWY 19; I BELIEVE HE MEANT TO ISSUE US ADDITIONAL INSTRUCTIONS TO FOLLOW ANOTHER ACFT. BY NOT ADDRESSING US CORRECTLY; WE FOLLOWED OUR LAST CLRNC (MAKE L TFC FOR RWY 19) AND CUT INSIDE ANOTHER ACFT INADVERTENTLY. NO TCASII RA OR TA WAS INVOLVED; AND THE OTHER ACFT CONTINUED THE APCH TO A LNDG. AS I PREVIOUSLY STATED; THE FREQ WAS EXTREMELY BUSY AND IT WAS VERY DIFFICULT TO COMMUNICATE EFFECTIVELY.