The major difference here is in who decides on the answers to the three basic economic questions. These are what to produce, how to produce it, and for whom to produce it. In capitalism, these questions are answered by market forces. In socialism, they are answered by the government.
In capitalism, essentially any good can be made by any company so long as enough people want to buy it at a price the company can afford. In socialism, the government decides what will be made and it decides how much of these things will be made. Socialist governments have things like "Five Year Plans" that lay out which goods will be produced. Socialist governments decide how the goods will be produced. They (and not factory owners as in capitalism) tend to run the factories and make the decisions about things like how many workers there will be and how they will be paid. Socialist governments decide who gets how much of the things that are produced. It is not like in capitalism where anyone who can afford to buy something is allowed to have it. In socialism, the government often rations things and determines who gets how much.