Both words are derived from the Greek krisis ‘decision,’ from krinein ‘decide.’ Events or circumstances are coming to a head, which implies a choice, having options.
Criticism is a choice between good and bad, ranking or rating. Criticism of anything, especially oneself, is usually a sign of ego. Judging by some self-developed or -adopted standard of right/wrong, beauty/ugliness. It is a way of assessing one’s own status in relation to the thing judged: better/worse, superior/inferior. Caring about these things is the domain of the ego.
Discrimination, however, as with Odysseus, is usually a sign of choosing the best option for achieving the Self. It is a move away from fragmented ego toward unity. When faced with taking this or that action, choosing the one that will lead toward the fatherland of Ithaka. It is letting go of the limited and moving toward the Infinite.
Of course this implies acknowledging that there is a fatherland, and having the desire to reach it. Most of us are so often under the spell of the suitors (of Circe or Kalypso), that this option doesn’t enter our thinking. We need a Tiresias to give us “a clear sign.”