In camera, all you can make is a JPEG greyscale photo, not a B&W photo.
They are not the same.
By making a B&W image from a color image in post processing, you have way more control over the contrast and tonal balance of the image.
As an example in Photoshop CS there is a B&W adjustment layer that allows you to adjust how the tonal quality of 6 colors is rendered in the final image. At the least in Photoshop one can adjust each of the RGB color channels to make a B&W.
In the days of film photographers were careful to not only choose the film they used based on how it rendered contrast, but they also put colored filters on the lens to do essentially the same thing pre process.
The main goal in making a nice B&W image is contrast control.