Several. The fact that the economic system of the early industrial period featured an arrangement of property rights which favored holders of capital (corporations exist only as ideas, but their owners are real beings) who then exerted disproportionate power over all institutions of society, including government, leaving those capitalists the dominant power in all domains of life is why critics of that early industrial economic system named it "capitalism", and the weaving together of corporate and government power driven by corporate influence over government remains a strong feature of capitalism. (Supporters of "capitalism" who have attempted to redefine "capitalism" to mean some ideal system of perfect market freedom rather than the actual system the term was coined to refer to often treat this as something other than capitalism, or as a failed form "crony capitalism".)

More formal integration of government, industry, and organized labor is corporatism, top-down forms dictated by the central government of corporatism were features of Italian fascism and many authoritarian movements of roughly the same time. This has sometimes led to the equation of corporatism with authoritarianism/fascism, though this is an error: corporatism is substantially older, and has substantially broader reach -- it is no more equivalent to fascism than anti-communism (also a feature of fascism) is.

And, despite the rhetorical differences in how the integration works, such integration is also a feature of those Leninist/Stalinist/Maoist Communist regimes that either don't go so far as to completely eliminate private industry, or which back off from it.

Which, taken together, illustrates the reason why there isn't a term in general use for corporations (which are, after all, creatures of government) and government weaving themselves together -- its a feature of every economic system that has actually practiced in which corporations exist, from capitalism to the various reactions against liberal capitalism.