The impeller fan has blades rotating around an axis and in general there is a reasonably smooth graph gas flow to resistance to gas, where the centrifugal fan again rotating around an axis but if you restrict the outlet the load often reduces, used a lot in motor vehicles as closing the vents reduces load, there are specials like the roots super charger which used lobes and a combination as used in the turbocharger, a special kind or turbine, turbine normally refers to many blades often one after the other with changing diameter as the air is compressed.
However there is not really a type which can't blow air over a distance, where I worked the impeller fan, often called axial fans, pushed the air 1 mile into the tunnel we were boring, clearly the so called axial fan (although since most rotate around an axis other than the roots types so most are technical axial fans) can push air a long way.
I assume an "an environment fan" is one of these
better know as a heat recovery unit? Often they are built into boxes
and use centrifugal fans, but the type of fan is more down to how to physically fit the fan in the heat exchanger box than if it can push air a long way.
Often the main consideration is sound, that fan in the tunnel sounded like a jet engine, which is after all a collection of fans, and when a fan can be triggered in middle of the night sound levels are important, at the moment I have the window open and a large fan blowing air through the house, because it is running for a long time, although sound level is a bit on high side, I only become aware of sound when it stops.
So the heat recovery unit running 24/7 you end up ignoring the sound, but when it starts at 2 am it wakes everyone in the house.
this fan is not centrifugal but clearly designed to duct air.
I over the last 3 years have lived in three houses, two with bathroom fans and one without, the two with fans we switched them off and never used them, the one without we wished there was a fan, and I sat back and wondered why, and realised it was the design of shower cubical, one house wide open space no curtains just a wet room, no problem, the other a small glass cubical which sealed at the bottom once you closed the door, no problem, the third was in the bath and the chimney effect caused the water vapour to circulate, in spite of an open window, this room caused a problem, OK before the shower, but once the glass panels were fitted and the shower in the bath mould was a problem, oddly in the town of Mold.
But you need to look at it as a whole, type of cubical for shower, how sound travels, length of duct, drainage of duct, if window in room, if that window opens, how replacement air enters the room, and where from, is that air pre-heated or from a cold area, and how dry or damp is that replacement air.