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I have perused the Aviation Instructors Handbook Chapter 6. From my reading and what I do with my students I would consider an assessment a formal evaluation of the students performance. A critique would be an informal evaluation and is usually part of the debrief after the flight.
I spend considerable time briefing the students on what the flight lesson is going to entail and the performance standards I am using, answer questions from study assignments and talk general pilot knowledge and things they need to know to become a great pilot and also to pass the oral test.
Once the flight is over, I spend time talking with the student on their performance. It is a one-to-one conversation where we both determine where the student is at and decide what the next lesson is going to be. This would be a critique.
I personally start out asking the students how they felt the lesson went for them... where things went well and where things need extra attention next time. I then start my critique where I describe what went well and what went not so well. At the conclusion we discuss what the next study assignment is going to be and the next flight training session is going to entail.
After the student leaves, I will sit down and formally document in the students training folder the items that we trained and the grades they received. This would be the assessment.
If I were to sum up this answer in a sentence. Critiques are informal discussions on performance and assessments are formal documentation of the performance.