In the 2 Live Crew case, the Supreme Court made a distinction between parody and satire. Because parody targets the original, it has a need, under fair use, to at least conjure up its target. Satire, defined as a broader, more socially, culturally, or politically-oriented spoof, was felt to not have the same need given that it is not directing its sole attention to a particular work. Satires are not precluded from fair use, but seemingly don't enjoy an initial leg-up that parodies have. There are other terms to connote a degree of appropriation from other works, but without a critical purpose. One such term is "imitation."
Lisa Pon explores imitation in Renaissance prints in her excellent 2004 book "Raphael, Durer, and Marcantonio Raimondi: Copying and the Italian Renaissance Print." The origins of parody also lie in imitation, and originally the term did not connote criticism or even merriment. This topic is explored in another 2004 book called "Early Musical Borrowing" edited by the improbably named "Honey" Meconi and for the very steep price of $95.
As a music major, I immersed myself in the music of the Renaissance Netherlands composers (like Ockeghem) as well as Italians like Palestrina, and Josquin de Prez, all of whom wrote dozens of "parody masses," masses that used secular music as an integral part of the polyphony. There were also cantus firmus and paraphrase masses that were also built on others' works. The borrowing was right up front, in the titles like "L'Homme arme" and Tavener's "Western Wind" mass. As Professor Meconi notes, "Borrowing is probably almost as old as music itself, and Western notated music is replete with examples from every time period."
Given this rich history, what is unusual is the underlying thesis of Professor Meconi's collection that "major questions" have arisen about "what constitutes borrowing, how we define the different types in use, what we call them, and why and how composers borrowed what they did. These topics have been the subject of a fierce and impassioned debate; this is not a field for the faint of heart."
Oddly, that makes me feel better when we mere lawyers try to sort out fair use according to labels: we're not alone in difficulties.