Regional Jet 900 (CRJ900)
Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP)
Confusion
ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Provided Assistance; Flight Crew Requested ATC Assistance / Clarification
Human Factors; Procedure
Tower cleared our flight for takeoff. When Tower instructed switch to Departure; I asked First Officer to query if we are supposed to do runway heading or RNAV. Departure stated RNAV and said that was our clearance; I told them we were instructed to takeoff but not told 'Climb via RNAV first fix' as usually included in takeoff clearance. Departure said that they do not need to state that; it is assumed; and he said they haven't been having any real problems for 2 months since they stopped stating the clearance.I told him that in CVG if they don't say cleared 'Climb via RNAV first fix'; you are expected to fly runway heading.We were not out of compliance of the RNAV; began turn; and flew RNAV as depicted.ATC uses non-standardized communication procedures. [I] found out some towers have been approved by FAA to not use 'Climb via RNAV first fix'; while others are required to state it. [This] creates a lot of confusion when the controllers are using different play books.The FAA [should] require Tower controllers to use standardized communication procedures at all airports. Meaning when they issue clearances; they do it the same way every time. This way; crews don't have to play the guessing game of what they want; when they want; or how they want.It would help greatly if the company would provide a list of which airports have been exempted by FAA to use standard radio phraseology so we can be aware of potential issues (threats) when we operate out of those specific airports.
Air carrier Captain reported a communication breakdown with ATC due to differences in usage of stating flying runway heading or flying RNAV.   .