Answer: the difference is a concept of human nature. Adam Smith´s philosophy is based on assumption of competitiveness. People are competitive, they comptete, there is a rivalry between them. All that presupposes individualism, autonomy, initiative, free spirit. Socialism lacks that. Socialism constitutes another sort of onesidedness: its point of departure is that people are good, like to collaborate and share. That is why socialism wants to eliminate all inequalities (that is why it was and perhaps still is attractive).
Explanation: of course things are much more complex. Adam Smith is a man of 18th century, socialism is a concept that was here and there everywhere and all the time with us, but never totally realized. Nevertheless ideas (even those that seem to be the most beautiful) should be always tested in reality.