Academic Marxism - or "Marxist Critique" - is really better referred to as dialectical materialism, historical materialism, or even more generally as Hegelian dialectics.

The political philosophies, namely socialism and communism, are a product of such thinking, but are not the same.

For instance, many feminists make heavy use of dialectics and are considered Marxist critique, but may not identify with e.g. communism.