Helicopter
Flight Crew Commercial; Flight Crew Flight Instructor; Flight Crew Instrument
Flight Crew Last 90 Days 213; Flight Crew Total 4178; Flight Crew Type 2476
Communication Breakdown; Situational Awareness
Conflict NMAC; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance
General None Reported / Taken
Procedure; Staffing; Human Factors
Flight started at the helicopter pads - second flight out of ZZZ for the day. This was a training flight with students. I was the Flight Instructor. I started up and prepared for takeoff as normal. The weather was IFR which required a SVFR clearance for our departure. I received weather and contacted Ground and requested the SVFR to the northeast with a present position departure from the helicopter pads. This was the expected as we had done so earlier. Initially; I was told to standby while the Controller was getting other aircraft taxiing. After the wait; the Controller came back and cleared us to the northeast at or below 1700 ft. via SVFR; which I read back. Despite still being on Ground frequency; I erroneously mistook the SVFR clearance as a clearance to takeoff as requested from present position. As such; I instructed the student to initiate the takeoff and depart; which we did.Our flight path was to the northeast which took us across Runway X; the active. As we reached 500 ft. and [was] approaching clear of the ZZZ Class 'C;' I expected a switch to Approach as usual but when I looked down at the radio I saw we were still on the Ground frequency. I quickly switched to Tower and was informed of my lack of takeoff clearance and additionally the overflight of an aircraft on takeoff from Runway X which we didn't see. Our departure flight path was at a 40-degree offset roughly 040; which put the start of Runway 8 behind us. Sitting on the right side; I didn't see Aircraft Y who was actually cleared for takeoff start their roll at roughly the same time as we did. Due to the angle; they were aft of my scan during the takeoff. Based on the info from the Controller; we passed over them by about 200 ft. as they were departing. Because we were still on the Ground frequency; we also didn't hear towers call to us when we started to depart without takeoff clearance. Unfortunately; all of this was caused by my assumption of having received a takeoff clearance and acting accordingly. Obviously; I should have been more aware and realized that it wasn't a takeoff clearance that was issued. I should have also noticed that we had not switched to Tower from Ground earlier. Not to pass blame; but an observation - it is common for a Ground Controller after issuing a clearance to push us to the next Controller; i.e.; 'Read back correct; contact Tower/Ground for takeoff/taxi.' This would seem more critical; particularly for a helicopter present position departure such as this one that does not require a taxi to a specific runway. In this case; that was not stated as far as I can remember. Additionally; there has been a lot of Ground and Tower combined frequencies lately and that also could have played into the confirmation bias that led to assuming my SVFR clearance was also a takeoff clearance and not switching to the Tower frequency. In this case; Tower and Ground were on different frequencies. Regardless; I have executed present position departures many times and not had an issue like this and I definitely made a mistake which almost resulted in a collision. In the future; I will exercise extreme caution and slow down to ensure this mistake does not happen again.
Flight Instructor reported mistakenly taking off without clearance which led to an NMAC event with another aircraft taking off.