As someone who considers himself a Social Democrat (as can be seen in my avatar sig), I think I disagree with that I bolded.
Social Democrats adhere to capitalism, they just want to practiced it with due social restraint. The main difference between Socialists and Social Democrats, is the economic means of production. As capitalists, Social Democrats - in classical textbook definition - would never preclude the economic means of production from private individuals. Whereas Socialists, as we know, remove the means of economic production from individuals. And this last, of course, is what freaks so many out (rightfully so!).
I believe "Democratic Socialists" might be the term for the attributes you're describing. Democratic Socialists, which unlike Social Democrats are indeed an offshoot of pure Socialism, differ by preferring a Democratic governance while keeping a Socialist economy. They, as you described, see Socialism as the goal - realizing they can't get there in one fell swoop.