A few basic terms are helpful to know. This is not an exhaustive list of nomenclature, just what we need to know to understand the differences between vessels.
A mast stands vertically from any ship that has sails. There can be more than one, depending on ship size and type. The center mast is the tallest and called the main mast. The mast at the bow (front of the ship) is the foremast and is shorter. The rear one, should it exist, is called the mizzen mast, and is the shortest. In a two-masted ship, the mizzen mast is the omitted one; however, the other two masts are farther back in the ship’s body.
Each mast will have at least one yard, to which the sails are attached. In many ships, the yard is horizontal. If perpendicular, or square, to the ship’s length, the ship is “square-rigged”. Most ships have from one to three yards of different lengths and thicknesses. By contrast, in lateen-rigged ships, the yard is sloped, running parallel to the ship’s length, one end pointing at the sky, and there’s only one per mast. The yards have names but these aren’t needed to understand this chapter.
Some ships have a combination of square and lateen rigging. This usually means the main and foremast are square while the mizzen is lateen. This will be mentioned further when looking at actual ship types.
In square-rigged ships, the sails are a trapezoid, being wider at the bottom than the top. On a lateen-rigged ship, a triangular sail is used. This is sometimes called fore-and-aft rigging because that’s how the yard is aligned (forward and aft, or rear). This rigging allows for a closer point of sail on the wind, being more maneuverable. It takes advantage of rapidly changing winds such as in the Mediterranean, but in the open ocean, winds are more constant and a square-rigged ship does not suffer a disadvantage. Sails can be configured in many ways, most of which will confuse anyone not familiar with them, but this resource goes into more detail: http://www.artofworldbuilding.com/sails.