What is the difference between a path and a stroke?

Is a path the set of points from a to b? And is the stroke the "definition" (i.e. the color, shape, etc.) of the path?

And, how can you have a path with no stroke? Is this only because it is a computer drawing program? In the real world you can't have a path without a stroke can you?

If it matters, I am using Inkscape.

Answer

A path, as you said, is a set of points. It is a set of coordinates that define a shape. The path itself is only a set of numbers, a mathematical definition, nothing more. Anything you see on your screen is a visual representation of that path.

A stroke is a visual attribute that you can apply to a path. A stroke can have a defined width, color or a number of other properties. A stroke is a visual effect that is attached to the path.

You can have a path without a stroke, but you can't have a stroke without a path.