What is the difference between a pine, fir, and spruce?

Most Christmas tree varieties fall in these three categories.

But I’ve noticed that the fragrance, branches and needles (not necessarily the overall form) of a Frayser Fir is very similar to a Norwegian spruce—and nothing like the Douglas fir which seems to be another type of tree altogether.

So what do Spruce, Fir, and Pine actually mean?