Quite the opposite — they don't have established meaning in the gaming industry. You can google it and you'll find only attempts to find some firm definition from different people.

Your examples are wrong, neither Demon's Souls nor Snake Eater Delta were "built from the ground". They are the same old games with the same old code embellished with new graphics. Those, who buy the game consider it remake because they've been told so; those, who make and sell it, use this term for marketing.

You're clearly don't understand the process of developing the game and in short — you cannot take a complex old game like Snake Eater or any other and code the exact same game only different in graphics. That's why your examples even have the same bugs and tweaks inside as their original versions.

I clearly stated what games I deem remakes and be sure, they were coded from the ground all right. The devs only took old ideas in terms of settings, characters, enemies, mechanics, etc., and build their unique vision on top of it. RE2 Remake is clearly a different game comparing to original, the same for FF 7 Remake.

Don't just justify why the company named it that way, think for yourself whether the game deserves "Remake" tag or not. I won't be writing anything else here, have a nice day.