A diamond is an entirely separate mineral species from corundum, with numerous gemological distinctions between the two.
Before getting into the differences, I would like to briefly touch on how many gemstones have been historically confused. Going as far back as the Greeks, or even further, there was no distinction between gems of the same color. Any blue, transparent stone was a sapphire, any red stone was a ruby, anything green and clear, an emerald, etc.
Amongst the most famous examples of this mix-up is the Black Prince Ruby. Despite the title of “ruby” (a variety of corundum) the ruby is actually a piece of spinel . It currently sits in the imperial state crown of Britain, front and center.
Like how corundum comes in the full rainbow of colors between its ruby and sapphire varieties (including colorless), diamonds can come in colors other than colorless like green, yellow, blue, and very rarely, red. This is where the similarities end though, starting with the fact they are colored by different elements. Unlike sapphires and rubies, colors other than yellow and brown in diamonds are very rare, accounting for less than 2% of all diamonds. This makes the following examples of finely colored diamonds exceptionally rare.
The most basic difference between corundum and diamonds is their chemistry. Diamonds are generally pure carbon with extremely small amounts of trace elements that can cause other colors in them, mostly nitrogen causing a yellow color. Corundum is made up of multiple elements, aluminum and oxygen (Al2O3), and is also colored by various trace elements.
Because of how these elements react to one another, they form different crystal structures. Diamonds have a very simple structure and fall into the cubic crystal system, growing in a bi-pyramidal shape (the Black Prince Ruby shows this growth habit too). Corundum is a little more complex and falls into the trigonal crystal system, growing in a spindle shape. Rubies do grow in a hexagonal shape too, but it is usually flat and shallow.
Unlike the cubic system; crystals in the trigonal system show doubling, meaning that the light inside the crystal visibly splits into two directions. This is formally called pleochroism, specifically dichroism for the two directions of light. While not visible in the colorless variety of corundum, it is a concern for sapphire and ruby cutters since it makes the gem show different colors in different directions.
In colored sapphires and rubies, the cutters must facet the stones to show their best pleochroic colors. As visible in R11385, the color through the top is much nicer than the dull, orangy-red seen through its side. This difference can dictate whole magnitudes of price.
A more widely known difference is that diamonds are the hardest mineral on earth, with corundum being the second hardest (not to be confused with durability, which is made up of hardness, toughness, and stability). The difference in hardness also causes a difference in luster, or how shiny a polished gemstone can be. Diamonds are the only minerals that show a highly reflective adamantine luster, though corundum does show a sub-adamantine luster due to its very high hardness.
Sapphires do not show fire the way diamonds do, which is why cut is not as important in them. This also applies to colored diamonds, where the fire can be obscured by their color. In these cases cut and even clarity are not weighted as heavily, though fire may still be visible in light colors like yellow.
Even though the color masks the fire, there are still colorful flashes of fire in the spectacular Tiffany yellow diamond. Directly contrasted with the diamond, the yellow sapphire Y4631 does not show the rainbow flashes. However, this improves any yellow sapphire’s color versus a diamond.