Monochrome is a single colour that describes photographs. A Monochrome image uses a reflection of shades and hues of the same colour. Monochrome is also referred to having a neutral background that highlights the single colour. The advantage of switching from grey-scale to Monochrome on your camera is that the camera's LCD screen displays black-and-white. This is really an acquired taste and photographers need to practice seeing the contrasts between colour and Monochrome.
Monochromatic colour is based on a single based hue and then applying its tints, shades and tones. Tints come from adding white and tones are achieved by adding darker colour like grey or black. This is not the strict scientific meaning and applies only to photographic workshop talk.
Photos that are only shades of grey are referred to as grey-scale or black-and-white. That said, they are also Monochrome. Monochrome photos are sometimes not grey-scale as they can have single colours like cyana, sepia or cobalt.