The more familiar steel-strung acoustic guitar is essentially derived from the classical guitar, so let's take a look at the main differences between the two designs:
The key difference is of course the type of strings used. The main ingredient in classical guitar strings was originally animal gut, but is now nylon. The upper strings are made from single strands of circular-section nylon, while the bass strings have a core of fine nylon strands with a soft copper alloy winding. Nylon strings have a much warmer sound than steel strings, even when played with a plectrum. Most classical guitar music consists of single notes and arpeggios - if strummed, the strings do not blend together as well as steel strings, so in classical guitar music, strumming is usually used as a particularly forceful effect rather than a standard ingredient.
The classical guitar features a 'slotted' headstock. The machine heads have rollers which pass through the slots in the headstock, rather than protruding at right angles as on most acoustic guitars. This design is also seen on some steel-strung acoustics, particularly small-bodied and the more ornate 'parlour' guitars.
The classical guitar neck is approximately a centimetre wider than that of most steel-strung acoustic or electric guitars, and does not taper from bottom to top. The fretboard is always completely flat. Classical guitars do not have a 'truss rod' - this was invented specifically for extra strength against the pull of steel strings. For this reason, steel strings should never be fitted to a classical instrument, as serious and usually irreparable damage will result.
Classical guitars rarely have fret markers on the face of the fretboard, but sometimes have dot markers on the side facing the player.
Steel-strung guitars vary greatly in shape, but classical guitars are more standardised. The vast majority of classical guitars are practically identical in size and shape, though a few luthiers produce slightly larger models. The instrument as a whole is generally rather lighter, as in addition to lacking a truss rod, the body also has less reinforcement.
The classical bridge is a rather simple device compared with other guitars. Classical strings do not have ball/bullet ends and are simply tied to the bridge. The bridge saddle is a straight piece of bone or plastic, without the intonation adjustment found on other guitars. Classical guitars usually have imperfect upper fretboard intonation, though this is not generally considered a problem, as in another key difference, the neck meets the body at the twelfth fret and is hard to access above this point.
Posture & Technique
Classical guitar teaching emphasises strict technique. Players play sitting down with the left foot on a footstool and the guitar resting on the left leg. The left thumb should not stray above a notional centre-line along the neck. In contrast, many rock players wrap the thumb around the neck to mute the lower strings, and sometimes even to fret notes.