CL604 CREW HAD ALT OVERSHOOT; AND TRACK DEV; DEPARTING TEB BECAUSE OF CONFUSION REGARDING ISSUANCE OF DEP INSTRUCTIONS.

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IN THE EARLY AFTERNOON OF AUG/THU/04; I FILED AN IFR FLT PLAN WITH LANSING (MI) FSS FOR A LEG FROM TEB; NJ; TO NEWARK; NJ (EWR); ABOUT 10 MILES AWAY. IT WAS FOR DIRECT ROUTING AT 2000 FT. WE PICKED UP THE CLRNC AT ABOUT XA00 HRS LCL FROM TEB CLRNC DELIVERY. MY READBACK READ 'ATC CLRS ACFT X TO NEWARK AS FILED; UP TO 3000 FT WITH (THE APPROPRIATE) 'SQUAWK CODE.' CLRNC DELIVERY REPLIED; 'READBACK CORRECT' AND GAVE A FREQUENCY FOR TAXIING. WE WERE CLRED FOR TKOF ON RWY 24 AND ASKED TWR FOR A 'DEP FREQUENCY' AS WE UNDERSTOOD THAT WE WERE NOT ON A PUBLISHED DEP. TWR GAVE US THAT FREQUENCY. AFTER TKOF; THROUGH ABOUT 800 FT AND CLBING; WE WERE HANDED OFF TO DEP CTL. WHEN WE WERE ACKNOWLEDGED BY DEP CTL; HE ASKED; 'WHERE WE WERE GOING?' WE REPLIED; 'RWY HDG TO 3000 FT.' HE ADVISED US TO TAKE 'A CLOSER LOOK AT THE DEP PROCS.' WE TOLD HIM WE WERE NOT ISSUED A PUBLISHED DEP TO WHICH HE REPLIED; 'THAT WAS VERY UNLIKELY.' AFTER A TURN AND IMMEDIATE DESCENT BACK TO 1500 FT; WE WERE CLRED UP TO 3000 FT AND THEN UP TO 4000 FT. HE SAID THAT HE HAD CHKED WITH TEB TWR WHO INDICATED THAT WE HAD BEEN ISSUED THE 'TEB DEP' IN OUR CLRNC. IN THE FUTURE; I WILL ASK FOR CLARIFICATION AT TEB ANYTIME I DO NOT 'RECEIVE/HEAR' A SPECIFIC DEP REFERENCED IN THE CLRNC. ON THAT DAY; THERE WERE NUMEROUS WX DELAYS AND GATE HOLDS IN EFFECT THAT CREATED QUITE A 'LOG JAM' OF DEPS AND ARRIVALS. CLRNC DELIVERY WAS VERY BUSY DURING OUR BRIEF STOP.