It depends a lot on what you actually mean by socialism and communism because these words can have very different meanings to different people and ideology.

As a very broad baseline, socialism is the socialization of the means of production, as opposed to the current privatization of those means. Now there are a lot of ways this could be done, and thus a lot of ways to define socialism. Some socialists want a strong State that can enforce strict rules of ownership, others want no State at all and a free cooperation between individuals, with a lot of variations in between. An anarchist, a communist, a social-democrat would all consider themselves socialists, even when they actually have very distinct ideologies.

Now communism, at least in its most recognizable form, is basically the end state of socialism in the Marxist ideology specifically. It designates a stateless, classless society in which each person contributes according to their ability and receives according to their needs. It’s basically the end goal theorized by Marx that has never been achieved yet in History.