True cinnamon is the inner bark of Cinnamomum verum, from Sri Lanka, and it is thin, pale, brittle and mild. Cassia is the bark of Cinnamomum cassia and its relatives, from southern China and mainland Southeast Asia, and it is thick, dark red, hard and much stronger. In most of the world outside Britain and Mexico, what is sold as cinnamon is cassia, and has been for a long time.
Both appear in Exodus 30. The holy anointing oil is myrrh, cinnamon, calamus and cassia in specified weights, mixed with olive oil, and the text is emphatic that the compound is not to be reproduced for ordinary use. Cinnamon and cassia being listed separately is one of the better indications that the ancient world distinguished them, whatever the modern spice aisle does.
In Chinese medicine cassia is rou gui, the bark, and gui zhi, the twig, and they are treated as different drugs with different actions. Rou gui is a major warming agent of the classical materia medica.
There is a practical reason to care. Cassia is high in coumarin, which is hepatotoxic in quantity, and several European food safety agencies have set tolerable intake levels that a heavy cassia consumer can exceed. Ceylon cinnamon has almost none.