I believe miso paste is made by mixing cooked, mashed, soy beans with a culture of koji (_Aspergillus sojae_), and a certain amount of rice, used to grow the koji, and letting it ferment.
Marmite is made by mixing malted barley with yeast (_Saccharomyces cerevisiae_) and a lot of water, straining it, letting it ferment, skimming off the yeasty froth that forms on top (you can discard the liquid, although i think people have found other uses for it), washing the froth to extract the yeast, adding salt to induce autolysis, filtering out the solid bits of dead yeast, boiling it down, and adding some seasonings.
So although they are both made by fermenting something, the process is quite different. Miso is mostly soy bean, modified by the fungus, whereas marmite is mostly fungus, and is much more processed and concentrated.
Instructions:
https://msmarmitelover.com/2011/04/how-to-make-your-own-marm...
Here are brief Wiki extracts:
"Marmite is a brand of savoury food spread from the United Kingdom, based on yeast extract invented by German scientist Justus von Liebig. It is made from by-products of beer brewing (see Lees (fermentation)) and is currently produced by British company Unilever. https://en.wikipedia.org/wiki/Marmite ..."
"Vegemite is a thick, dark brown Australian food spread made from leftover brewers' yeast extract with various vegetable and spice additives. It was developed by Cyril Callister in Melbourne, Victoria in 1922. ..."
A spread for sandwiches, toast, crumpets and cracker biscuits as well as a filling for pastries, Vegemite is similar to British Marmite, New Zealand Marmite, Australian Promite, MightyMite, AussieMite, OzEmite, German Vitam-R, and Swiss Cenovis. https://en.wikipedia.org/wiki/Vegemite."
Special note to Americans: Vegemite is owned by Kraft, a US multinational. So you're to blame for foisting it on the world!
That's one for books, but as far as I recall Kraft was there from the outset in the 1920s (so it was really always US-owned until recently).
Edit: just checked the low-salt version (both are used here—it's the smaller jar) and the label is different. Never noticed that until now.
Miso I know less about but my wild guess would be it's some sort of by product of trying to preserve food.
It’s made from seaweed and soy sauce but I’ve found it to be very similar to marmite
https://japanesetaste.com/products/momoya-gohandesuyo-nori-s...
They're both salty and brown. Otherwise they have little in common.
It didn't quite work for me. Miso flavour turns out to be very compatible with toast but my test miso didn't have enough tang to cut through properly, so the impression it left was dominated by salt. Marmite and relatives are salty as well, but they have more bite in the flavour.