Correct, as far as I can tell. "Gulyás" is a soup, with lots of water. It has pieces of beef, potatoes, carrots in it, among other things.
"Pörkölt" has little to no water. It is close to a stew, but with lots of paprika.
And "Paprikás" is kind of like a "pörkölt", but with "tejföl" (sour cream) added.
That is my idea of these. But I am no cook, so I am sure I am not exactly correct on these.
Furthermore, while "gulyásleves" is kind of standard, there are "gulyás" variations, like "babgulyás", "bográcsgulyás".
"Pörkölt" can be made from various meats, beef, mutton, pork, chicken, it can even be mushrooms, or fish, etc. It is a kind of making the dish that "pörkölt" represents. I think it has to do with lots of onions and paprika.
"Vörösboros marhapörkölt" is kind of a "must try", put it on your bucket list if you want.
And, as I said, you can add sour cream to the sauce of a "pörkölt", and turn it into a "paprikás".
Apologies to anyone who can actually cook and is outraged by what I just wrote. :)