300mm is REALLY 300mm on ANY camera. But 300mm will have a different field of view, depending upon the size of the sensor/film plane.
As a rule of thumb, a normal lens is one that provides a normal, non-magnified viewpoint - and is generally considered to be about the same as the diagonal of the image frame.
On a 35mm film or FF digital camera, a 300 mm lens has a focal length that is about 7 times the diagonal of the 35mm frame (~ 43mm) So, effectively, 300mm provides about 7X magnification compared to NORMAL perspective when used on a FF or 35mm camera.
Whereas on 4/3, a 300mm has a focal length that is about 13.3 times the diagonal of the 4/3 frame (~22.5mm). thus, when used on a 4/3 sensor, the same 300mm lens now provided about 13.3X magnification compared to NORMAL perspective.
It's the SAME lens, with the SAME focal length. But the relative magnification it provides is bigger, the smaller the image frame it is used on is. And yes, even though the apparent magnification is greater on the smaller format, the compression of the perspective between foreground and background is unchanged for the 300mm lens no matter which format it's used on.