Okay, so extremely abridged, here is what seperates capitalism from socialism.

Under capitalism, private individuals own the means of production, distribution, and sustenance. Workers are forced to go to one of these private individuals and exchange their labor power for a wage. Capitalist profit is generated by paying the worker less than their labor power is worth but enough to sustain workers as a class. The workers are prevented from using the means of production without entering into the wage labor model through the threat of physical violence.

Under socialism, the means of production are managed in common, somewhere along a sliding scale of the people working in a workplace and democracy having control of how the workplace operates depending on the system

You'll note that these both can operate within markets, and both require at least some planning.

Video: we need a mixture of capitalism and communism is bullshit

Book: Explaining why markets are bad

Edit: this is ignoring the way the state plays a role in these economic formations but Im trying to keep it simple.