"Criticism" vs. "critique"

What is the difference in meaning between criticism and critique?

At bottom there is no difference.

The terms critic, criticize, criticism have always had a double sense in English. The base meaning is “pass judgment on”, but in popular use the words have usually meant “pass a negative judgment on”, while in academic and literary use they have tended in the opposite direction, signifying close and dispassionate analysis which may or may not issue in a formal judgment.

The French version critique was adopted into English primarily as a noun, meaning an instance of criticism, a critical essay or notice; in many cases there is no evident distinction between critic(k) and critique in this sense until the 19th century. Around 1960 academics began using critique in both nominal and verbal senses more and more frequently—at a guess, as a desperate effort to drive into thick undergraduate heads the fact that the critical endeavour in literature, art, history and philosophy is not simply a matter of expressing negative opinions.

If that was the intention, it failed. Today critique in popular use is just as likely to mean ‘censure’ as ‘analyze’.

“Maybe we should be that way about the first gentleman also and really critique the way they look all the time, their choice of tie, or their hair style or whatever, or maybe their weight.” —Former first lady Laura Bush on CSPAN, Jan 27 2014

Yes, to hell with all of these left communists making criticisms! For as we all know the left has never done anything worth of critique! —Comment on a book review on The North Star, Apr 5 2014

Funding freeze critiqued A UK science-advocacy group says that a repeated freeze to the government's £4.6-billion (US$7-billion) science-research budget, announced on 26 June, will damage early-career researchers' work and drive them to other nations. —Nature online, 2013