I mean, you’re precisely on the right track, which is why no country has ever claimed to be communist. They’ve all claimed to be at various stages of socialism with the end goal of achieving communism. Economic systems are extremely complex, as are the core differentiators between them. There’s rarely a way to cleanly claim “this is true of a capitalist economy but not of a socialist economy” and have that apply to the real world because most economies lie somewhere between free market capitalism and end-stage socialism. The words are horrendously overloaded and have no meaning in comparisons between actual countries. You’re mapping a binary statement onto a spectrum.
Having read Marx/Engels, I really do think Smith is a good place to go from there. Not necessarily because his ideas are great, but because it provides a lot of context for the world in which Marx and Engels were writing from.
Edit: perhaps the cleanest way to differentiate the systems is in their goals. Marx writes “From each according to his ability, to each according to his needs” implying some degree of central planning to improve the lives of people, while Smith writes “By pursuing his own interest he frequently promotes that of the society more effectually than when he really intends to promote it” implying that people are “led by an invisible hand to promote an end [for the betterment of society].”