To transform something from one coordinate system to another, create a transform object using Transform.ChangeBasis.
For example, if you need convert a 3-D point from world x-y coordinates to Windows screen coordinates, you would use a change of basis transformation.
If you had a point in Rhino’s camera coordinate system and you need it translated into world x-y coordinates, you would use a change of basis transformation.
If you had a point in 3-D point from world x-y coordinates and you wanted to report to the user what that point was in construction plane coordinates (of the active viewport), you would use a change of basis transformation.
If you wanted to orient an object oriented from one plane to another plane, you would not use a change of basis transformation. Rather, you use a plane-to-plane transformation using Transform.PlaneToPlane. This is because you are not looking to convert from one coordinate system to another. You are simply looking orient in the same coordinate system.
Hope this helps.
– Dale