I’ve just double-checked the etymology, so I believe this is correct:
Originally, there was pottage.
“Pottage” was just whatever you had gathered and mixed together into a pot, and boiled for a while. Usually, it would be a mix of (probably) salted meats, herbs, vegetables, and grains of some sort (oats, barley, millet, whatever). It’s what most people ate most of the time and there was no real one recipe, it just depended on what was in season, what you’d caught, etc. If you look globally, pottage is the majority of historical food everywhere, even if they don’t call it that, including everything from Korean Yukgaejang to Indian curries to North American Succotash whatever the predecessor of Chupe was. It’s just a very efficient way of cooking, while busy doing other things. Grilling requires you to spend your time paying attention and the same with baking; you’ll burn it if you don’t get your timing right. Stews are forgiving.
At some point, puddings were invented: wrapping up all of your pottage in a bag and letting it hang, dry out, and harden. This gives us everything from fruitcake to blood pudding to (possibly?) sweetbreads. I’m not aware of similar inventions outside of Europe?
In Europe and Asia, breaded sheaths were also invented to contain your pottage, so you could carry it out into the field while you work, and eat it later - the bread serving like a sandwich baggy. Think of things like potstickers, Samosas, and Cornish pasties. But, back then, the bread would be hard and possibly mostly inedible. You might just throw it away after slurping down the innards. Granted, I don’t know for sure that potstickers are evolved from something with a hard shell, but I’d say it’s a pretty safe guess.
Anyways…pottage, pudding, and pasties are sort of “the world of food” at the point in time the US split off from the UK and that’s where much of the confusion comes from.
A big part of the change brought on by the Enlightenment and its technologies (the printing press, scientific thought, ovens with moving parts, etc.), in the culinary world, was a push to create actual recipes and things with names. Similar things happened with everything else. E.g., we went from having a handful of colors (red, blue, green, etc.) to suddenly having several thousand named colors with very specific definitions that could be transmitted to someone else and have them be able to recreate the same color just by knowing the part of the light spectrum and the brightness (or whatever).
“Pottage” was a very vague thing, that covered a wide variety of foods, as did pudding and everything else. As things started to be broken out and given their own labels, some words went away (like “pottage” itself) and others became used for very specific things which used to be a large category (e.g., corn - originally meaning a “grain” in the sense of a grain of sand, a grain of salt, a grain of maize, etc.). And that depended widely on region. An American biscuit is different from a British one, as is a chip, as are pants.
Porridge is just the word pottage, mispronounced. Maybe it was a regional variant of the word? Maybe it was a cutesy version of the word that came to mean a more breakfasty version of pottage? Hard to say without doing a bit of hunting through old books. (I leave that to others.)
But so the answer to the question depends on where and when you’re asking about. Even if you mean modern day, I suspect that it still varies by region. US? UK? Australia?
As a modern day, West Coast American, porridge is something like Cream of Wheat. Oatmeal is bits of oat that have been allowed to soak in milk or water, and eaten like a soup.