Corundum is an aluminium oxide. Varying amounts of titanium, iron, or chromium ions can replace the aluminum, but some aluminium must always be present. If the oxide simply consisted of iron and oxygen and had no aluminium, then it would simply be hematite.
Corundum with plenty of Chromium is generally red. When the resultant crystal is also very translucent, it is called a ruby. Ruby is sometimes used loosely to describe all red corundum, whether it is gem grade or not. Corundum which contains titanium and iron has a much wider colour range, but is typically some shade of blue. This is described as sapphire when it is translucent. Again blue corundum is frequently sold as sapphire, even when it isn't gem grade.