Marble has two meanings. First is that of the gene. It causes the fish to turn different colors, sometimes over the period of a few hours and sometimes a few months. But it is typically a drastic change like red going to black or white going to blue (most common). We call those that change, a Marble. The second is the "Marble" coloration which is usually a splotchy kind of color like the Koi's, that's a sub type of the marble. Those are the "Fancy Dragons" you'll see on aquabid and typically they will "marble" out as we call it and change their colors. Red based fish (red koi) will always marble out to red and then typically black, fairly quickly. Yellow based koi tend to keep their patterns a little longer before turning their body yellow but keeping the black, white, and blue markings over top.
Grizzle is not under the marble pattern or gene. Grizzle actually comes from the Pastel genes. They are typically stable fish and will have a salt and pepper look to them. Unlike the Marble who is splotchy and has bigger patches of color, the grizzle has little patches of color.
Photos for difference:
Grizzle:
Female Grizzle:
You'll note that most grizzles end up being blue/white/flesh tone based but they will usually not "marble out" and turn all blue. There are exceptions of course. Any fish can carry the marble gene regardless of their first color combination.
And this is a marble, not denoted by the red splotch but by the bigger splotches of blue and white. He could also be called a Koi due to the pattern but he'll marble out too quickly for that to stick.
You're correct on Piebald, it should be a flesh toned head. Monster is another similar coloration but with white on the head instead of flesh toned. People often misuse them and say that flesh toned is white but it most definitely is not.
Here are pictures to help out. This is a Piebald Betta. He does have a splotch of red up there but he's still a Piebald. Piebald actually does come under the marble gene (as does Butterfly, Koi, and Fancy). But for the most part, Piebald's tend to be stable which means they won't marble out typically. Again, there are always exceptions.
And here is a Monster. Monster will always be a Full Mask Dragonscale (thick scales that cover the entire body, including the head).
And unlike Piebald, this is unstable and so he will eventually turn all blue with black as the base color
Your Archie would actually be a Multicolor because he does not fit in any specific category. Typically if they fit into one category, they won't fit into another unless it's a subtype of that category (Black Devil and a blue/red/black Triband fish are essentially the same things). He has Black Scale Edging which is not a trait in the Grizzle. He doesn't have enough scale coverage to be a Grizzle either, they typically have full irids where Archie only has partial (where the blue is on top of his body is the iridescence part, the bottom is not covered). He does have white scaling on his head but it doesn't cover the whole thing so he can't be a Monster, that white will eventually go blue though. And then his fins have cellophane (clear) and the blue you see are the iridescence on the membrane between the rays which makes it shimmer. So, he is a marble under that all but not in the sense of the coloration, but that he has the gene and will go blue down the road.