Word-Order – The Difference in Path Phrasing

the doesn't belong here - there is more than one grave so with 'the grave' it would never be clear which one is meant.

Correct would be to say

A board was stretched over each grave and people, in groups of 10, were standing on it.

Or:

A board was stretched over each of the graves and people, in groups of 10, were standing on it.

I think you've hit the nail on the head in the comments. (By the way, let's note that this discussion is entirely about the order of pairs of nouns. If one of the words is an adjective, there's no question the adjective comes first in English. In "the color red," "red" is a noun, but in "the red color," it's an adjective, just like "the red car.")

To help clarify, these constructions have a "category" and an "instance" of a thing in that category. So in "the movie Titanic," the category is "movie" and the instance is "Titanic." Similarly, "variable" is the category and "foo" is the instance.

I think you've hit on the answer: what makes the difference is the degree to which the "instance" can work as an identifier on its own—a name, a title, a proper or "proper-ish" noun. Could you leave the "category" word out of your sentence and still be understood? If so, the category should probably come first. "Let's watch the movie Titanic" could equate to "Let's watch Titanic," with little need even to establish the context of movies. As the answer about Die Hard shows, when the instance really is a true proper noun (a unique title, etc.), putting the category second changes the meaning (making the instance work like an adjective).

Many of your examples could go either way, but the order could give a slight alteration in emphasis. For "file extension" and ".jpg," I might put the category first if the emphasis was on jpg: "Filter for the file extensions '.jpg' and '.png.'" But the reverse if the emphasis is on "file extension": "Don't confuse the 'jpg' folder with the 'jpg' file extension." Similarly, say I have a script named "setup." If I say, out loud, "Run the setup script," I could be using "setup" as an adjective and the script might actually be named "init_setup." But if I say "Run the script 'setup,'" I'm clearly using its name.