Two instruments are sold under this word, and this site covers both. The Puerto Rican cuatro carries ten steel strings in five doubled courses on a body with a pinched waist, and is played with a pick. The Venezuelan cuatro carries four single nylon strings on a small box and is strummed, usually with a damped stroke that stops the sound as much as it starts it. They are not variants of each other.
Telling them apart in a listing
Count the tuners in the photograph. Ten means Puerto Rican; four means Venezuelan. If the photograph is too small, look at the outline: the Puerto Rican instrument has a distinct waist and a larger body, and the Venezuelan one is small and comparatively square-shouldered. Sellers outside both traditions use the word loosely, so trust the hardware rather than the description.
Checking a Puerto Rican cuatro
Ten steel strings pull hard. Sight the neck for a bow, look at the top behind the bridge for a bulge, and check the nut: each course wants two evenly cut slots close enough that a pick strikes them as one. Uneven pairs are the common fault and they make every figure on the golpe pages harder than it should be. Then turn all ten tuners and listen to each course played alone.
Checking a Venezuelan cuatro
Four nylon strings are gentle on a body, so the checks are different: the neck should be straight, the frets should be level, and the instrument should sound when strummed rather than clacking. Because the characteristic stroke is damped, listen specifically to a muted strum — a well-made instrument gives a clean percussive attack with pitch inside it, and a poor one gives a dull slap.
What applies to both
Buy the instrument you can hear before you buy the one you can only read about; play something you know, even one shape from the chord library; and treat cosmetics as the last consideration rather than the first. Neither instrument is expensive at the entry level, and both are commonly built well at that price by makers who make nothing else.