Both nouns refer to a small, exclusive group of people. Clique suggests a fairly closed group of people, often forming within a larger group, whose members have similar interests or status. Clique has a negative connotation, and suggests an association based on a sense of superiority to everyone else (a clique of popular kids) or on a desire to hold all the power: the ruling clique. Coterie can have positive or negative connotations. It can suggest a close-knit circle of friends, artists, scholars, or scientists: a literary coterie. Coterie can also suggest an exclusive set of people who associate with a prominent person, whose coterie it is: surrounded by her coterie of advisors; his loyal coterie. Here there’s more potential for elitism. As with ruling cliques, powerful coteries in government are usually undesirable, unelected holders of power.