Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP)
Confusion
ATC Issue All Types; Deviation - Altitude Excursion From Assigned Altitude; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Air Traffic Control Issued New Clearance; Air Traffic Control Provided Assistance; Flight Crew Requested ATC Assistance / Clarification; Flight Crew Returned To Clearance
Airspace Structure; Human Factors
I was pilot flying. After we crossed ZZZZZ at 11;000 feet; the controller gave us a descent down to 7;000 feet. We then changed frequencies to 128.75. The next controller gave us a descent to 6;000 feet and said after ZZZZZ1 to join the approach. We thought we were cleared for the approach after ZZZZZ1 because he did not say to join the localizer; so my FO (First Officer) called to clarify what the instructions were. The approach plate said ZZZZZ1 is at 7;000 feet; and we were confused as to why the clearance was 6;000 feet. The controller verified 6;000 feet and join the approach after ZZZZZ1. After ZZZZZ1 we started a descent to 3;700 feet as published; when the controller called us and said we weren't cleared for the approach. We were in a critical phase of flight with a heavy workload when he told us to write down a phone number. We then thought we had been given a heading of 010 and were trying to call to confirm but he was overloaded talking to other aircraft and kept asking us to write down the phone number for the possible deviation. We had started our turn northbound and conditions were VMC at that point with terrain in sight. He then came back and gave us a new heading and asked us to climb to 5;000 feet We complied with all instructions and landed back [at our destination] safely with no further event.Unfortunately; there was a communication error between us pilots and ATC. We were trying our best to clarify the instructions given; however the phraseology used in terms of join approach instead of join the localizer contributed to the mistake. Also; the second error when we turned the wrong direction was a result to being given a phone number during a critical phase of Flight; high workload environment and the frequency being tied up when we were trying to confirm instructions.
[Report narrative contained no additional information.]
EMB-135 flight crew reported that due to a communication error between pilots and ATC there was confusion when instructions stated to join the approach not clearance for the approach.