Well, right after an Indigo Bunting we get an American Goldfinch. What a happy coincidence! It allows us to compare the two easily, and careful comparison is needed to distinguish these two aurally. The goldfinch is generally less disciplined than the bunting, but if you find a less exuberant goldfinch, one who limits himself to two of a kind, he could tempt you to say "bunting." It does happen.
First, the similarities. Both species produce notes that are stretched out vertically on the sonogram. This gives them a "sweet" quality, which makes them pleasingingly muscial to human ears. This is despite such dramatic frequency sweeps having no place in human-produced music. Second, these vertical notes and phrases are quite brief. Third, said phrases are often repeated.
And now the differences, which are not dramatic. The bunting only repeats once, a goldfinch can do several renditions of a phrase. The bunting has a single song, some parts of which he can omit, perhaps to produce a little variety, but the goldfinch has many phrases, which he can arrange in any order. I don't actually know if that last statement is true. You could find out, just as you did with the Red-eyed Vireo. Is the relative order of each pair of phrases, whether they are continguous or not, always the same? There are two more cuts on Ebird, which will increae the sample, should you choose to accept this mission.
Finally, a few words about beauty. Did you know that the goldfinches are in the same family as canaries. So, the beauty of the goldfinch song is not surprising. Now take a look at one. The American Goldfinch is among the most brightly colored members of this family of northern finches. The Indigo Bunting is an entirely different family, one centered in the warmer parts of the Americas, and he of course is strikingly pleasant to look at as well, albeit with cool colors rather than hot ones. Convergent songs, contrasting colors. We are lucky to have so many of these beautiful songsters, both kinds, among us. Wouldn't want that to change.