One is more coloquial.
"I want my photo on black and white". Nobody says "I want my photo on grayscale". "Black and white photography", not "grayscale photography".
But if you want to get technical, I'll post a list of some terms.
Grayscale It is a file of one channel of information. It can be 8 bit or 16 bits, but only one channel. Normally this channel is interpreted as a gradient from white to black. (It could contain another channel but for transparency, not color) (C)
It is not necessary printed in commercial print with black ink, you can use another color, but you get a monochromatic image, for example, a sepia image. (D)
A "black and white" photo could be made on an RGB image only if you desaturate it completely. It could look the same but it is not because it contains 3 channels, not only one. (B)
On Photoshop a one-bit image is called "bitmap" which I think is wrong, but on other programs, it is called "black and white", which technically it is wrong too, because with one click you can use another ink. But the difference is that you do not have gradients. (F)
Sometimes a grayscale image can be confused with an 8-bit image. An 8-bit image has a palette, which can be a grayscale palette, but in reality is just a palette. The values of each square are still rgb. (E)
Technically just C and D are grayscale. The other ones can be simply black and white.