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You probably think of monochrome as black and white and the shades of grey in between, i.e. that monochrome is the same as a black and white image. This is how it is often used, but monochrome means that only one color or hue is present in the image.
“Chromaticism” is the greek word for color. So monochromatic underlines that only one color is present. You can of course have different versions of that color by having different tints (adding white) and shades (adding grey/black) to the pure color (hue).
I think of monochrome and monochromatic as being one and the same, but this is not entirely correct. However, for practical purposes working as a photographer, I think this assumption works just fine.
You can work to achieve monochromatic images by using colored filters or post processing the image or a bit of both. Personally, I use Lightroom to tweak my images to a monochromatic look.
The reason for using a monochromatic color scheme is to simplify the image and take out some distractions. If you have a scene where there are many different colors, reducing the variety of colors down to monochromatic can help the viewer to see more of the structures and textures in the image, and help the scene appear more calm.