Ductility vs. Malleability vs. Toughness vs. Brittleness

Ductility is the property of metal with the ability to stretch so it bends, but does not does not break. When you stretch steel it breaks when you bend it and copper does not. So copper is ductile, steel is not.

Malleable metals like aluminum can be pressed. You cannot stretch aluminum as well as copper, but you can press it between rollers and make sheets so fine that it makes aluminum foil. You can also squeeze copper, but not quite as thin, as it will tear. Copper is not as malleable as aluminum.

Incidentally, Sir Humphry first spelled it alumium in 1807 then changed it to aluminum, and finally settled on aluminium in 1812. Americans and Canadians spell and pronounce the name aluminum, while the British and most of the rest of the world use the spelling and pronunciation of aluminium.
Toughness is about how strong metal is after processing. Toughness is not only how much force can you apply before it snaps, it is also a question of whether the metal has some bend before it breaks. This is called "deflection". Steel is tough so you do not pound it into shape, because it just dents and malforms.

Hardness is about withstanding impacts and pressure. Steel, as opposed to quartz, is not hard; and it is not brittle. Steel cannot take as much pressure pushing against it as quartz or diamonds; it will bend or malform and will also break sooner. The end result of that pressure is brittleness. So steel has good hardness and low brittleness.

Quartz has high hardness, high brittleness, low toughness. What this means is that it takes a lot of pressure or a very sharp, fast strike to break it, and when it breaks it snaps or shatters. Quartz has no malleability and no ductility. Under heat and/or pressure, it breaks. The quality of shattering instead of breaking cleanly is brittleness.

Bottom line, copper ductile, aluminum malleable, steel tough, quartz brittle.