Both words refer to removing someone from danger or difficulty. Rescue is the more general term. It suggests the saving of a person or thing from harm or death (rescued the cat from the fire), and usually involves physically removing someone from danger and bringing them to safety. Extricate suggests freeing someone who is caught or trapped in a literal or figurative tangle. Not as straightforward as some types of rescue, extrication is often done carefully, with difficulty, or finally (at last). Some of the most frequent objects of extricate are victim, body, and driver, and the context is often a car wreck or a disaster. Extricating a country is also a common challenge—whether from a war or from debt. On the lighter side are the hairy social situations from which we often have to extricate ourselves—politely, or gracefully.
Both nouns refer to disrespectful or contemptuous words or actions that wound another’s sense of self-worth or pride. Most typically, an insult is a harsh disparaging remark that expresses low regard for someone. Insults are hurled, shouted, or traded like blows. Affront suggests an open show of disrespect towards a person, a group, or a collective value. Your aunt might consider it a personal affront to her that you didn’t let her know you were in the neighborhood, but parked right in front of her house. An affront can offend a specific human attribute (an affront to their dignity or sensibilities), and can be applied to a value (Regulation is an affront to liberty; an affront to democracy or our fundamental rights). Adjectives often paired with affront include serious, blatant, and egregious.
Both words refer to making an idea or thing clear or comprehensible. Explain emphasizes the act of giving a complete account of something. After a teacher explains a concept, she might then quiz students to see how much they have understood. Whereas you can explain something badly and then try to explain more fully or in more detail, elucidate implies that clarity is accomplished (whether or not the reader or listener is able to see it). Elucidate refers to making something clear or more clear for others, as if shining a light on or through it—a speaker, a book, a series of studies, or research results are typical subjects of elucidate. Typical objects include a mechanism, relationship, role, or structure—concepts or processes more complex, perhaps, than those that can be exhaustively explained.