Analogy vs. homology is how biologists draw family trees. Determine that a feature is homologous, and you can pin that species to a branch pretty surely. If it's an analogous variation, or if you can't tell which it is, it's a wild card, basically. If you don't distinguish between the two, you can come up with some pretty crazy biology pretty quickly—elephants related to goldfish because they both have two eyes, for instance. But if you think about it, when it comes to music, we tend to assume that all variations are homologous.
In part, that's because it's a safe bet—homologous variations fairly outnumber analogous variations in the comparatively finite world of music. But even when variations do arise independently—Schoenberg and Rufer both hitting on dodecaphony, for example—we attribute it to something "in the air," that it was historically time for such a development. It's hard to disprove that sort of analysis. Sometimes it really is just a case of a common evolutionary goal. But I think that there are also developments that blur the analogy/homology line; I also think there are composers who turn that blur to their advantage.
One of the more interesting musical evolutions is that of ragtime. Classic rag form is rather odd and open-ended:
|Theme:||A A B B A||C C D D|
It's somewhere between the daisy-chain form of a generic Strauss waltz and the refrain-driven form of other 19th-century dances. But where most of those dances would round off the form, bringing back the initial theme and key at the end (like, say, the "Una Schottische"), classic ragtime lops of the refrain at the end, leaving you hanging both tonally and thematically.
You might think that the form evolved that way because the sequence of themes evolved into a cumulative enough progression that the return of the refrain became superfluous. But actually, it was the formal variation that came first. Scott Joplin's early rags try out all kinds of possibilities, but never fully round the form. "Original Rags" (1899) starts and ends in G major, but arranges its themes A-B-C-A-D-E. "Maple Leaf Rag" (1899) uses the classic A-B-A-C-D form, but puts the final D in the original key, A-flat major. But both display the more interesting feature: the penultimate theme is more brilliant and "final" than the final theme (Joplin even marks the D theme of "Original Rags" double-forte and "Brilliant"). Compare the last two themes of "Maple Leaf Rag":
The C theme stays high and fully voiced; the D theme descends to the middle of the keyboard and, in the right hand, almost completely avoids octave doubling. That's a fairly consistent pattern in Joplin's early output.
But between 1907 and 1909, Joplin writes a whole series of rags—"Gladiolus Rag," "Pine Apple Rag," "Fig Leaf Rag," "Wall Street Rag," &c.—where he makes the open-ended form a virtue. The D theme of "Gladiolus Rag" is typical:
The final theme now uses the fullest voicing, the widest range, the strongest and most repetitive syncopation, and the most adventurous harmony (both "Gladiolus" and "Pine Apple," for example, feature prominent shifts to the flatted submediant in their final themes).
Our natural instinct is to analyze that as a homologous variation—Joplin must have got it from somewhere, perhaps the cavatina-cabaletta sequence of Italian opera, or perhaps Rossini overtures, or perhaps similarly obsessive passages in Chopin or Schumann. But the fact that he doesn't arrive at this stylistic point until he's been tinkering with the form for a decade or so implies, at least to me, that it was a reaction to the limitations of previously-evolved rag form, not an inspiration from outside—an analogous variation, in other words, not a homologous one. And remember that we're also hearing the shift in light of ragtime's transformation into jazz, where such final-theme characteristics do become homologous; the climactic, riff-driven shout choruses of both stride and pre-bop big-band swing can trace their lineage directly to Joplin's triumphant D themes. (Interestingly, Joplin seemed to abandon classic rag form once he mastered it—the last two rags published in his lifetime, "Scott Joplin's New Rag" and "Magnetic Rag," are fully-rounded thematically and tonally.)
One of the reasons Joplin's rags are considered such paragons of the style is because such analogous features sound homologous—the illusion of idiomatic and organic inevitability within the form is so strong. You could populate an interesting subcategory of composers with a particular flair for that kind of sleight-of-hand. But even within that category there would be variants. Francis Poulenc, for instance, conjures by mixing an analogous vocabulary with a homologous rhetoric. Robert Schumann almost does the exact opposite.
Schumann's op. 39 Liederkreis, on poems by Eichendorff, seems at times to be a cycle-within-a-cycle, some of the songs commenting on or echoing other songs. The first shift in the cycle comes at the third song, "Waldgespräch"; the first two songs have set place and mood, but all of a sudden, the singer is telling a fairy tale about the witch Loreley, luring a traveler to her castle. The melody ends with a cadential figure, sol-do-mi-re-do:
The key relationships in "Waldgespräch" recall those in the first song in the cycle; likewise, the key relationships in the fourth song, "Die Stille," recall those of the second. "Die Stille" end with the same cadential figure as "Waldgespräch":
The eighth and ninth songs in the cycle are another reminiscent pair, with harmonic and motivic connections to the sixth and seventh songs, respectively. (In addition, there's a strong literary echo of the seventh song, "Auf einer Burg," in the eighth, "In der Fremde.") "In der Fremde" brings the cadential figure back:
The ninth song, "Wehmuth" (which brings us back to the E-major tonality of "Waldgespräch") ends with a variant of it:
It might seem like a stretch to say that Schumann intends to link these four songs (possibly along with another, "Mondnacht," which ends somewhat similarly) merely through this stock cadential figure. But here's the thing: that figure turns up nowhere else in Schumann's song output. This is one of the keys to Schumann's ability to deploy the analogous as homologous: his unifying motives are often so, well, obvious that you barely notice them. And yet here, they signal the boundaries of a sophisticated, experimental embedded narrative in the style of Schumann's literary hero Jean-Paul Richter. (Which would explain the inverted character of the cadence in the ninth song, the singer emerging blinking from fantasy into reality.) The vocabulary is homologous, but it's treated in a highly analogous way.
Given the often-indistinguishable visceral audience reactions to both extreme serialism and extreme minimalism, I think you might be able to make a case that the big shift in mid-20th-century experimental music was not so much a matter of vocabulary, but that composers no longer felt the need to try and massage the analogy/homology divide. Take for instance, the difference between Philip Glass and John Adams: where Adams, with his hints towards jazz and Impressionism, is deliberately asserting a taxonomic relationship with various established genres, Glass's music, especially outside of a dramatic context, usually seems more concerned with internal proportion than external lineage. Features that resemble other musics are presented as analogous developments from within the technique. Music in Twelve Parts is a particularly fine example of this: the work's ontology recapitulates a highly personal interpretation of tonal phylogeny.
Music, like other creative endeavors, is different from biology in that decisions regarding analogy and homology can come from both without and within, as if organisms had as much say in the classification of a variation as taxonomists did. The tree of music seems to expand and contract in cycles—at the moment, new music seems focused on homology, leaves at the edges rather than whole new branches. But if history is any indication, that will change at some point—the most vital evolutionary trees, after all, are the least orderly ones.