A short video below featuring Marxist economist Richard Wolff on what he sees as the difference between capitalism and socialism. Wolff is always thought-provoking and good to listen to, even if one doesn’t agree with everything he says.
For me, it is helpful to see capitalism around the world as coming in many varieties, each with strengths and weaknesses, and as an evolving system, rather than as a pure type. Capitalism hasn’t always existed, and it may transform into something else given time. This would not necessarily be socialism. This line of thinking draws on (old) institutional economics.
Having said that, the essentials of the employment relationship, extensive market exchange, production by firms for profit, private ownership and a legal system which supports individual property rights seem to me to be important in a definition of capitalism. For an in-depth discussion of these issues I can recommend Geoffrey Hodgson’s recent book Conceptualizing Capitalism.