Cavaliers vs. Roundheads
“Cavalier”, as a term, was probably popularized (with respect to the English Civil War) in the late 1630s or early ’40s, already carrying a derogatory connotation and often appearing alongside the term “Royalist”. The root of the word itself comes from the Latin caballarius - “horseman” - from which chevalier and caballero are also derived. The Cavaliers were probably skilled riders (some of them, anyway), but they are best remembered for their extravagant, elaborate fashion and hairstyles - this, at least, was the image that history has preserved, thanks to artists like Anthony van Dyck. The Parliamentarians and Puritans intended for the word to paint the Royalists as frivolous, dissolute, and hedonistic, though it was eventually rendered obsolete as a political term in the late 1600s, replaced by “Tory”.
“Roundhead” surely was a knock on the short, cropped hairstyles of some of the Puritans, in contrast to the Charles II-style ringlets that were popular with the so-called Cavaliers. According to some sources, this was the case, as an authority describes a crowd in Westminster in 1641:
They had the hair of their heads very few of them longer than their ears, whereupon it came to pass that those who usually with their cries attended at Westminster were by a nickname called Roundheads.
Oliver Cromwell himself wore his hair longer than the typical Roundhead. Like “Cavalier”, the term applied only to a portion of the enemy faction; in this case, only the military and non-Independent Puritans could logically be called “Roundheads”. And, like “Cavalier”, “Roundhead” was succeeded by a different, more modern term - “Whig”.