Most black and white photography is done with digital cameras, which always shoot in color, or rather take three filtered black and white images: through red, green, and blue filters.
Then the image gets converted into black and white, usually in computer. (I can NOT see any reason to set your camera to shoot black and white — you can always "black-and-white-ify" later, but you can never bring back the lost color.)
There are so many DIFFERENT ways to convert color images to black and white that it is mind-boggling. Even Photoshop alone gives you about 10 ways. Here are some examples of different BW aspects of a color image.
Bottom Line: There are different ways to convert an image to black and white and the results can be very different.