The colour gamut (or simply: gamut) refers to the range of all colours in a colour space that can be recognised (camera, scanner) or reproduced (printer, monitor) by a device.
It is visualised in the form of a colour solid.
A colour profile stores the characteristic features of a colour processing device.
These can be scanners, printers and monitors.
With the help of colour profiles it is possible to see what kind of colour range a device can represent.
A colour space is based on a colour model, and is its concrete application to a colouring method (printer, monitor, etc). It therefore contains all colours that can actually be represented through this method and the associated materials.