Gulfstream G200 Captain reported smoke and fumes in the cock pit during climb. The flight crew performed an air turn back and landing at departure airport.

Narrative

First flight was a repositioning short flight from ZZZ1 to ZZZ with no passengers. The first flight was finished normally without any abnormalities. Second flight of the day. Route IFR International Flight ZZZ-ZZZZ. Standard departure. Standard initial climb. While crossing FL 180 for FL 410 I started to sense a strange smell. Initially; the smell was more of a very strong humidity; no burning smell or visible smoke as this time. As I am starting to figure out what the smell is and where is coming from; my partner also mentions he feels a strange smell.While we are both trying to figure out what the smell is and where is coming; the smell started to shift more into smoke smell and you could start to see smoke in the cockpit. At this point; I called for oxygen masks and goggles on. We stopped the climb (around FL 200); [requested priority handling] with ATC and started the return back into ZZZ.We ran the Cockpit or Cabin Fire / Smoke checklist; by the time we got to dump the cabin (procedure from the checklist) most of the smoke went away.As we were approaching the airport; we realized we were still too high for the approach and we decided to do a right 360 to lose some altitude. We prepare the approach for RNAV GPS Runway XXL approach. Right after landing; we exited the runway; parked the aircraft and proceed to evacuated the passengers. The evacuation was done on Taxiway. (ATC was advised that we were going to do so). Fire team arrived immediately.Unfortunately; while evacuating the passengers; an airport security pickup car arrived with a person who interfered with our evacuation. A very strange situation; this person was demanding to see our pilots license; medicals and driver's licenses while we were still evacuating the passengers from the aircraft. Passengers were evacuated with no injuries.Maintenance Company forms were submitted and Safety Director of the company was contacted. Notes:- By the time of landing; we were unable to confirm where the smoke was coming from. I would say that I believe the smoke was coming from the airflow out from the lower vents at the bottom sidewalls next the passengers' feet. (not confirmed)- No hazardous materials were on board the flight.