Some time in the 1960s the color temperature of the calibration light source was changed from 2800 K to 4700 K. It was suggested that the change would allow the discontinuation of requiring a daylight and tungsten EI for films.
The spectral sensitivity of the photo cell has always played an important role with meter accuracy. Two meters could disagree simply because of the difference in sensitivity to the color temperature of the light source. Also, most photo cells are sensitive to infrared. If the material reflects a lot of infrared it will effect the reflective meter while the incident meter is unaffected. A simple test for infrared sensitivity can be done with any remote. Point it at the meter and monitor any changes.
Chan Tran was right about how a reflective exposure meter has a greater chance of matching an incident meter when the incident meter is used with the disk. They should be about 1/2 stop difference when using the dome.