Let's start with the difference between criticism and a critique.
Criticism is negative comments - identifying faults or bad points. A critique is simply an evaluation - it can comment on the good points and/or the bad points.
My project idea received a lot of criticism from my colleagues - they said it would never work.
In his critique of the book, Johnson praises the excellent character development, but says the plot moves too slowly.
A critic is a person. There are two types of people who are critics:
A professional critic is someone who specializes in evaluating art, films, or literature: an art critic, a movie critic, etc. This type of critic makes critiques
A critic in general is someone who tends to find negative things and point out faults. This type of critic likes to criticize (meaning to make criticism -negative comments). The president's critics say he is not devoting enough funds to national security.
The word critical also has two meanings. When describing a person, it means the person is finding fault:
My mother was always very critical of my work - she said I would never be a good writer.
When describing a thing or situation, critical means "essential" or "extremely important":
The baseball player made a mistake during a critical moment in the game, causing his team to lose.
Access to clean water is critical to the health of the population.