Also you're going off mainstream liberal dictionaries and not how the left as a cluster of organized movements has come to definitions for its working purposes. So you're coming at it from an outside (liberal) perspective which reads as an indicator you're a liberal.

The problem with dictionaries is that they describe the popular use of a word, not necessarily the academically correct one. I only used the dictionary because it was honestly too easy to do a gotcha there.

A great example of dictionaries being "wrong" is the word "factoid". A factoid originally is a popular piece of information that is actually incorrect or false - a popular lie. Now the word factoid is in many dictionaries described as being "an insignificant or trivial fact", which is like, the exact opposite of the original meaning of the word. I'm 100% sure that in certain universities, I would be marked down for using "factoid" as "fun fact", even though dictionaries seem to think this is fine.

The original meaning of the word Social Democrat was a heavily discussed topic even in the beginning of the Soviet Union. After WW2, it was even popular within Socialist/Communist circles to call SocDems, "Social Fascists", as the enabling of the SocDems in Germany (SPD) helped the Nazis attain power, since they positioned themselves against the rest of the "left". SocDems will always rather align themselves with capital, rather than the "actual left", because the entire ideology reinforces capitalism. The reason people are mad at you here, is that SocDems have historically, every single time, helped the fascists rather than the socialists when push comes to shove. It's the reason for the quote "Social Democracy is the moderate wing of fascism". Now you can disagree with that last part, but this is history. Schumacher did betray the socialists. And he always would have, because Social Democracy is a capitalist ideology, which is why Marxists refuse to let them call themselves socialists. You cannot believe in capitalism, and socialism at the same time. They are opposites.

DemSocs on the other hand, are Reformist Socialists. They are who the dictionaries should actually refer to. They are the people who believe that a peaceful reformist transition from capitalism to socialism is the way to go, even though it has never worked. They believe that if you just vote hard enough, the capitalists will just let the poor take away their power. I don't actively dislike them, but I think it is very very naive.

Marxists are usually Revolutionary Socialists, who believe in revolution as a way to make change. This has worked several times in history, and there are several countries in the world right now that still exist after a socialist revolution, and are doing as well as you can considering that the entire western world is sanctioning them.

Marx hated Social Democrats btw. When one of the founding figures of the ideology does not think that a Social Democrat is a socialist, then I dunno what to tell you.

In short, the dictionaries are wrong. In an academic setting those definitions would be rejected instantly. People just do not understand what these ideologies are, so they use the words the wrong way. These words get used the wrong way enough, and the dictionaries will change to fit, as that is what dictionaries do. But the original meaning, that is part of the books that many of us read about these subjects, do not match with the dictionaries. If you referred to dictionary definition in a Political Science class, you would not pass, I assure you.