Pilot reported both PFDs were not reporting accurate information and requested vectors for a diversion and precautionary landing.

Narrative

Our clearance out of ZZZ was 'ZZZZZ5 departure; ZZZZZ transition; maintain 5;000 feet. On the ramp we both verified that the FMSs were in the right position. Upon take off we got instructions to 'RNAV ZZZZZ1'. I was PF (Pilot Flying) and I had NAV in the Mode select panel and we both verified that FMS1/2 on both PFDs (Primary Flight Displays). Soon after takeoff I was following the command bars and began a turn to the west to what we assumed was ZZZZZ1. That is when Name noticed the sign on the FMS 'INDEPENDENT FMS OP' had illuminated. I was on a heading of 270 when ATC said; 'There is traffic; fly present heading and maintain 2;500 feet.' I immediately descended about 100 feet because we had already flown through that altitude; leveled off and hit HDG on my Mode select panel and engaged the auto pilot. At this point we had no idea there was anything amiss yet and we simply thought the new heading and altitude was due to traffic. Afterwards he gave us DIRECT ZZZZZ2 and notified us of a possible deviation. We were both surprised because to our knowledge we had complied with everything. I then noticed my side was acting a bit off (even with the autopilot select set to my side; my VS; HDG and any commands I put into the Mode select panel were not being acknowledged by the airplane) but we thought Name's side of the map and FMS was accurate so I transferred controls to him and he began flying off his PFD. ATC asked us if we were DIRECT ZZZZZ2. We said; 'yes; we are'. A minute later ATC queried us again and said we were showing about 25 degrees to the right of course and gave us a 350 heading to ZZZZZ2. He also mentioned that ZZZZZ2 was actually over the ZZZ1 VOR and we had completely missed it BUT... it was still showing us on track; about 30 miles to the north of us. Shortly after he then gave us DIRECT ZZZZZ3; we entered it into the FMS and on Name's side it looked good. ATC confirmed; 'I show you turning towards ZZZZZ3'. Soon there after; ATC once again said we were; 'off course and direct ZZZ2 instead of ZZZZZ3'. That is when we both realized BOTH of our FMS's were askew. I immediately told ATC that we needed vectors and could not go DIRECT TO any fixes. He notified the next controllers of our issues and we did a visual approach to Runway XXL into ZZZ2. We stopped using the MFD map as soon as we realized it was inaccurate. I did some dead reckoning and used my ForeFlight moving target to find the airport and other landmarks. Name landed uneventfully.