What you’re asking is essentially economic governance. Who plans the economy?
In a capitalist state, these are the CEOs, boards of directors and the like who plan production.
In a socialist society, there are options.
The early Soviet Union experimented with what is usually called syndicalism (from French word for trade union: syndicat). Meaning that economic planning is done by trade unions. The problem there is that industries had a hard time coordinating during times of civil war.
This is why USSR moved to state economic planning to create the broadest possible coordination.
As an aside, some capitalist countries also heavily relied on the state for planning (I think it’s called dirigisme?). In a socialist country the state is controlled by the working class, so production aims to improve human wellbeing first, rather the profitability of industry.
In Yugoslavia, we saw a form of market socialism. The economic planning was done on the scale of individual worker cooperatives, who participated in market relations with each other.
In China and other current AES states we see an economy broadly planned by the state, but still relying on private sector for some industries (also similar to early Soviet NEP).
You asked for a chart but I think that’s hard to do (and maybe even counterproductive) because there are no clear divisions between these forms of planning. Usually it’s a mix of things, we just look at the dominant form. Also charts often end up reinforcing "ideology supermarket" attitude. It’s good to force oneself to look at each countries conditions individually. As materialists, we should evaluate each economic model based on its usefulness for the specific time and place.
Ask, who plans production? Which class participates in this planning? Etc.
Hope it was helpful and let me know if you want to follow up on anything!