According to Wikipedia, Darwin believed that the birds he was studying were "a mixture of blackbirds, 'gros-beaks' and finches", but "The ornithologist John Gould soon announced that [they] were, in fact, twelve separate species of finches."
But Gould himself also appears to have been somewhat wide of the mark; the birds now known as Darwin's finches (a.k.a. Galapagos finches) belong (again according to Wikipedia) to the tanager family and are not closely related to the true finches. The tanagers are the world's second largest family of birds, after the tyrant flycatchers, with 240 species; they live in South and Central America. (The tyrant flycatchers are found throughout the Americas.)
On its Finch page, Wikipedia lists several other groups of birds that are "commonly called 'finches'" but are not true finches.
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