Monochrome and black and white and grayscale are used randomly these days for the same grayscale thing. Even though strictly speaking Black and white is 2-shade images, monochrome can be any single colour (like old monitors in yellowish), and grayscale is the real term people are looking for.
The computation from the bayer pattern is usually using the Y component from the Y'CbCr compressed image. It can be different in your model but I doubt it. It is a weighted sum of the R,G,B values based on human sensitivities. It is how yellow gets brighter than cyan and magenta (pure mean of R,G and B will result in a dark gray for yellow).
Y = 0.299*R+0.587*G+0.114*B