To quote Wikipedia's excellent answer:
A triangular sail, extended by a long yard, which is slung at about one fourth of its length from the lower end, to a low mast, this end being brought down at the tack, while the other end is elevated at an angle or about forty-five degrees; -- used in small boats, feluccas, xebecs, etc., especially in the Mediterranean and adjacent waters. Some lateen sails have also a boom on the lower side.
Trapezoidal, actually. But the square sails were called square sails. Lateen or square could be referred to as yards.
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They were referred to as "four-cornered" sails.
I'm not an expert, but I believe you can sail closer to the wind with a lateen-rigged sail than with square sails.
Instruments: Lateen sails Improvments: Caravel
Lateen Sails
Triangular-shaped sails helped catch wind from the sides and rear.
The lateen is believed to have been used in the Eastern Mediterranean as early as the 2nd Century ce (common ear). The effective use by the Arabs caused it's rapid spread through the Mediterranean. The lateen sail was so popular because its ability to sail into the wind. Prior to the lateen a majority of sea vessels used square sails (which one can imagine wouldn't sail into the wind very effectively). The lateen made up a majority of ship sails during the Age of Discovery (When Columbus discovered the Americas). The lateen made it possible to sail faster, farther, and more efficiently. An elite ship during the Age of Discovery was the caravel, its elite status can be attributed to how effectively it utilized the lateen sail.
Square sails are not truly square but rectangular with a longer long side on the bottom perimeter of the sail. They were and are referred to as "four-cornered" sails.
One type is the "lateen sail", but there are also jibs; Genoa & spinnaker.
A caravel is one of the ships Columbus sailed in that has 2-4 masts and lateen sails.
Lanteen sails were used by the ancient Egyptians and many other Mediterranean countries too