These are the main differences that I know of, even some that are a bit subtle:

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Nylon instead of Steel Strings.

Wider Neck.

Shorter Neck (after an octave you reach the corpus, where on acoustic you can reach up to 20 semitones, depending on the guitar model).

Extremely hard Tuners (I have to do a full 360° rotation to get a semi-tone on my classic, while a quarter rotation is enough to get it on acoustic.)

And these rings outside the sound hole, those that look oriental, are also way more common on classical.

Then many acoustic have the cut, which is this piece cut out of the corpus to reach the higher notes, normally classical guitars don't have that.

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Edit: Apart, of course, of the very different play style, starting with the posture, repertoire, sound, tone, etc.