Both are members of the insect order Lepidoptera, but moths belong to the "classical" group Heterocera, whereas butterflies belong to Rhopalocera.
Though this classification is no longer used (because the "moths" don't constitute a natural group), it highlights a useful character to distinguish moths from butterflies: the antennae of butterflies are club-shaped (thin, with an expanded tip), while those of the moths are more diverse and often feather-like.
This figure shows the typical shape of butterfly and moth antennae:
http://cache.eb.com/eb/image?id=63162&re…
In general, moths have "fat" bodies, covered with lots of hair, and inconspicuous colors, while butterflies are more brightly colored, and their bodies are thinner and hairless. However, there are exceptions: beautifully colored moths, as well as drab butterflies.


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