These words have several different meanings as both noun and verb, but each may refer to a passage or scene selected from a book, play, or article. Basically, to excerpt is "to pick out," "to pluck," whereas to extract is "to remove, often with force": "The professor read us an excerpt from the novel." "From this poem, please excerpt your favorite lines." "Don't extract the wrong meaning from my remarks." "The dentist will soon extract this bad tooth."
Dictionary of problem words and expressions. Harry Shaw. 1975.