An exaptation is just one example of a characteristic that evolved, but that is not considered an adaptation. Stephen Gould and Elizabeth Vrba proposed the vocabulary to let biologists talk about features that are and are not adaptations:
A feature produced by natural selection for its current function (such as echolocation in bats).
A feature that performs a function but that was not produced by natural selection for its current use. Perhaps the feature was produced by natural selection for a function other than the one it currently performs and was then co-opted for its current function.
For example, feathers might have originally arisen in the context of selection for insulation, and only later were they co-opted for flight. In this case, the general form of feathers is an adaptation for insulation and an exaptation for flight.
“Contrary to earlier prejudices, there is nothing inherently progressive about evolution.” – Richard Dawkins