Ok so first thing to know is that the frame is acting as a unit. The connections between the beams and columns are fixed, so the forces are moving through the frame differently than if there was a pinned connection between the beam and column. Because the frame has fixed connections your reactions are going to occur at the base of each column and the load will be divided equally between the two columns.
The second thing to keep in mind is that moment forces are a combination of force and distance. The distance that you use is the one perpendicular to the force. In this case that is the height of the column. If we were looking at a beam with a gravity load, then you would use the length of the beam .
So ultimately yes B and C have the same moment. Again because this is a frame the moments will be highest at B and C and tapper off to 0 towards A and D.
For more information on frames check out Chapter 15 of Form and Forces by Edward Allen.
Additionally, there is a helpful diagram at this website: https://theconstructor.org/structural-engg/analysis/analysis-of-moment-resisting-frame-lateral-load-distribution/1720/