Diffraction gratings

Just a question about the naming of optical phenomena.

I’ve taken these explanations from a book I’m using:

Diffraction is when a single wave passes a slit or obstacle and spreads out. The single wave produces a diffraction pattern.

Interference is when we have more than one source of coherent waves which combine together at a given point. Their phase difference determines the intensity at that point.

These definitions make sense in terms of the interference pattern formed in Young’s double slit experiment, and the diffraction pattern seen from single slit diffraction. However, what about a diffraction grating – the above seem to imply it is an interference phenomenon producing the lines.

Can anybody please explain the idea behind this naming – or is it a good idea to not worry too much about the names? Thanks.

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