The two examples are temporal inverses of one another. In the situation of capitalism collapsing into government-granted monopolies, free-market capitalism is the first stage, and state central planning is the second stage. In the situation in China, the first stage was a vanguard-party-led society governed by a dictatorship of the proletariat that carries out state central planning, and the second stage is mostly free-market capitalism.
I don't think that anyone ever tried to use "Leninist system" to mean "a system where the government is not corrupt", but maybe I just haven't read enough of Lenin?