Masonry is both the name of a type of construction material and the way of using that material. Generally, masonry refers to laying individual stones, bricks or blocks bound by mortar to form the bulk of a building. Some form of masonry is used in most construction.
Brickwork is one of the most common types of masonry in modern times. Brick masonry is used in home construction, and in many public buildings like schools or fire stations. The typical pattern of brickwork is two horizontal bricks side by side alternating with a brick laid 'transverse' to the wall---one end facing out instead of the side. Brickwork generally provides good insulation. Also, it helps reduce building costs because exterior painting is not required.
Veneer masonry creates a thin layer of brickwork that acts and looks like solid brickwork, but in reality is about one-fourth the thickness of brickwork, as stated on Masonry Planet. Veneers are used to create external or internal walls, usually to add a decorative or functional (thermal) element. A veneer is built around a core support wall, sometimes made from wood or metal, sometimes from concrete.
Serpentine masonry is laid in a so-called "crinkle-crackle" line instead of a straight line. Serpentine masonry is far stronger than straight brickwork and more topple resistant as well, according to Global Oneness. For this reason, serpentine masonry can be laid in a single thickness of bricks, or laid unreinforced.
Stone masonry uses either dressed or undressed stones. Dressed stones are usually made into uniform sizes, and laid much like brickwork, except in a single layer. Undressed or rough stones are laid in a style called rubble masonry, which fits together unevenly shaped and irregular-sized stones to form a wall.
Concrete blocks are a newer style of masonry and typically utilize large blocks of concrete laid in a similar way to bricks. Because of their size, concrete blocks are much faster to lay than bricks and are often the support wall of an exterior brick veneer.