There is a very interesting notion of “critique”: it begins with Kant and stretches through Marx in the German philosophical tradition. In fact, it is most developed in Marx when he says he develops a “critique” of the “science” of political economy, a “critique”, which, he says, is nonetheless a “science”. He does not develop a “scientific critique” of political economy: he develops a critique of the science of political economy.
There is another notion, a rather trivial one, of critique that continues in the German philosophical tradition: beginning with the Frankfurt school and continuing to this day with writers like Habermas and Sloterdijk. It harks back to Kant’s use of the word in some senses, but is nowhere as developed as it was with Hegel’s pupils.
There is a third notion of critique that the French philosophers like Sartre used. Here, it merely signals a philosophical affiliation and mostly substitutes for the more commonsense notion of criticism.
The fourth notion of critique is merely a ’learned way’ of saying ‘I object’. It appears that this is how many post-modernist writers employ the word ‘critique’.