Diamonds from Africa. (crystal at lower left is ~2.5 mm across)
A mineral is a naturally-occurring, solid, inorganic, crystalline substance having a fairly definite chemical composition and having fairly definite physical properties. At its simplest, a mineral is a naturally-occurring solid chemical. Currently, there are over 5200 named and described minerals - about 200 of them are common and about 20 of them are very common. Mineral classification is based on anion chemistry. Major categories of minerals are: elements, sulfides, oxides, halides, carbonates, sulfates, phosphates, and silicates.
Elements are fundamental substances of matter - matter that is composed of the same types of atoms. At present, 118 elements are known (four of them are still unnamed). Of these, 98 occur naturally on Earth (hydrogen to californium). Most of these occur in rocks & minerals, although some occur in very small, trace amounts. Only some elements occur in their native elemental state as minerals.
To find a native element in nature, it must be relatively non-reactive and there must be some concentration process. Metallic, semimetallic (metalloid), and nonmetallic elements are known in their native state.
The element carbon occurs principally in its native state as graphite (C) and diamond (C). Graphite is the common & far less valuable polymorph of carbon. A scarce polymorph of carbon is diamond. The physical properties of diamond and graphite couldn’t be more different, considering they have the same chemistry. Diamond has a nonmetallic, adamantine luster, typically occurs in cubic or octahedral (double-pyramid) crystals, or subspherical to irregularly-shaped masses, and is extremely hard (H≡10). Diamonds can be almost any color, but are typically clearish, grayish, or yellowish. Many diamonds are noticeably fluorescent under black light (ultraviolet light), but the color and intensity of fluorescence varies. Some diamonds are phosphorescent - under certain conditions, they glow for a short interval on their own.
Very rarely, diamond is a rock-forming mineral (see diamondite - www.flickr.com/photos/jsjgeology/14618393527).
The rough African diamonds shown above display the two common crystal forms - cubes and octahedrons (= double pyramids). The yellowish-gray specimens are cubes to slightly mis-shapen cubes. The two clearish specimens are octahedral diamond crystals with inclusions.