"From your comments it appears that you have two definitions of what is a socialist?"
My comments said nothing about my definition of "socialist". I was wondering about your definition. Your definition of "socialist" apparently includes the regimes of North Korea and Iran, but does it include those who suffered under the Nazis, like the late president of the Socialist International, former German chancellor Willy Brandt?
If your definition of "socialists" includes both opressives fundamentalist regimes like Iran's and those who opposed the Nazis to defend democracy, your definition is quite useless, as it would cover those and everybody in between. Does it cover anarchists too? It already seems to cover everybody from radical democrats who are willing to die for their beliefs to those who kill radical democrats. I don't see much that Willy Brandt and the mullahs in Iran have in common. Perhaps you do? Or perhaps your definition of "socialist" doesn't include the most prominent socialists of the western world, and is actually quite the opposite of what "socialism" means as defined by socialist parties like Brandt's?
It is strange that those who refer to themselves as socialists actually opposed the very regimes that you refer to as socialist, isn't it? And they did so when nobody else would. Conservatives, liberals, nationalists, they all supported Hitler, but (self-proclaimed) socialists did not. Hm...
This whole comment is rather off-topic to the original discussion, of course, but since you asked...
Hitler's party was called "Nationalsozialistische Deutsche Arbeiterpartei" (short "NSDAP"). The German word "Sozialismus" comes from "Sozius" which is a Latin/German word for "partner". It refers to partnership, not an economic system (as the English word "socialism" does, the German of which is also "Sozialismus"). "Nationalsozialismus" means that all members of the nation should work together, the word still has nothing to do with the economic system envisioned by Marx. "Deutsche" means "German", of course, and "Arbeiterpartei" means "Worker's Party", which is an odd name, since labourers were underrepresented in the party. It was a party of civil servants and teachers, mostly. Labourers voted socialist rather than national socialist, which is why the NSDAP was weak in cities like Berlin (many workers) and strong in more rural areas (no industry).
And, yes, Hitler did imprison the supporters of the socialist parties. Refering to both them and him as if they belonged to the same group would be an insult to the victims, I think.
As for Stalin, I do not know how much of a Marxist he really was. He didn't seem to believe that the proletariat should rule (since he wanted to rule himself) and he didn't seem to want government to whither away (he was rather a very strict statist). If you want to know my opinion, it is that one shouldn't believe Hitler when he claimed to run a worker's party (which had few members that were workers) and one shouldn't believe Stalin when he claimed that in his country the proletariat had the power (since it was him who had the power).
Some people simply aren't very honest about these things, chief among those deeply immoral fanatical murdering tyrants.
As for the differences between Karl Marx and Hitler, ideologically, I see one difference in as much as Marx did not, afaik, advocate the killing of Jews for the heck of it. It simply wasn't a part of his ideology.
Hitler did not, btw, consider himself a "socialist like Karl Marx", because Hitler spoke German and knew that "Nationalsozialismus" wasn't "Sozialismus" (the economic system). He did, in fact, consider socialism his political enemy. And if you don't understand the ideological difference between trying to defend democracy against a dictator (which is what the Marxists of the time did) and murdering millions of innocent people just because they were Jews, I'm not sure how I can help you understand my point.
Some people have taken to using the word "communist" (which originally meant the more anarchist version of "socialist") to describing the likes of Castro and "fascist" to describe the likes of Hitler (and the Syrian dictator seems to fit here too, as did Saddam). But refering to them all as "socialists" is using the name of their victims to describe the criminals, and that is insulting the victims and a very wrong way to remember their sacrifices, no matter how you spin it.