Failure refers to something that is not successful: The party was a big failure; I was disappointed by the failure of my idea. A failure is hard to take, but there are worse things—like a fiasco, which refers to a usually public failure so complete that it is disgraceful, humiliating, and sometimes bordering on the ridiculous. A wedding reception at which the vegetarian option contains lamb, the air conditioning breaks down, and the newlyweds get into a screaming match and leave in separate cars would be a fiasco. Some of the most typical phrasing found with fiasco is also found with words like “scandal,” “controversy,” and “affair.” For example: this whole wiretapping fiasco could have been avoided; Remember last year’s state fair fiasco involving the goat milk judges?
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.
Both words refer to setting something going or putting it in motion. Start has a wider range of usage. We can say someone starts a car, starts a club, or starts an argument. Instigate, which derives from a Latin root meaning “to prick” or “to goad,” refers to prompting a human activity by urging or spurring it on. The object of instigate is usually an act of aggression or hostility (instigated a riot; instigated a war), so the word tends to have a negative connotation. However, instigating change is one common and more positive use, and both instigating a project and instigating a discussion are also fairly common and less negative.