MU300 FLT CREW TAKES CLRNC MEANT FOR ANOTHER ACFT ON THE TEB 5 DEP.

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ON DEP FO WAS FLYING THE TEB 5 DEP OFF OF RWY 24. UPON CONTACTING DEP THEY TOLD US TO MAINTAIN 1500 FT. I ASKED IF THEY WANTED US ON THE RWY HDG AND HE RESPONDED 'NO' HDG 280 DEGS. THEN I HEARD HIM SAY TURN TO HDG 300 DEGS CLB TO 10000 FT. I READ BACK THE CLRNC AND THE FO BEGAN TO CLB. A SECOND ACFT SAID THAT WE HAD READ BACK THEIR CLRNC. I TOLD THE FO TO GO BACK TO 1500 FT. AT THAT TIME WE WERE AT 1700 FT. WE IMMEDIATELY WENT BACK TO 1500 FT. THE CTLR ASKED ALL OF US TO PLEASE LISTEN. I FELT THE COM WAS POOR DUE TO NON-STANDARD PHRASEOLOGY AND HIGH WORKLOAD WHICH LED TO CONFUSION. I FEEL THAT PROPER COM/PHRASEOLOGY WITH BOTH PARTIES WOULD HELP RESOLVE THIS ISSUE. THE ATC SPECIALIST I FELT SHOULD HAVE ASKED US TO FLY THE SID AND NOT HAVE SAID MAINTAIN 1500 FT. FURTHERMORE; I THINK WHAT HAPPENED IS THE CLRNC TO CLB AND TURN WAS GIVEN THEN THE ACFT CALL SIGN LAST WHICH WE DID NOT HEAR AND TOOK FOR OUR CLRNC. HOWEVER; WE WERE UNDER HIGH WORKLOAD AND MAY HAVE NOT HEARD THE CLRNC PROPERLY. ONCE AGAIN I FEEL USING PROPER PHRASEOLOGY WOULD RESOLVE THIS ISSUE.