I constantly hear about caramelization, like in onions, which I believe have fairly high sugar content. However, I heard it in the context of beef today (Every Way to Cook a Hamburger (42 Methods) | Bon Appétit). Is the chef referring to the caramelization of sugar in the beef patty or the caramelization of something else? That is, does caramelization always refer to sugar?
Caramelization is defined as the pyrolysis of sugars. Pryolysis is decomposition due to high temperature. So, yes, caramelization is always an effect on the sugars present in an ingredient. The Maillard reaction, as pointed out in a comment above, also contributes to flavors and browning when cooking. However, the Maillard reaction specifically refers to the interaction between amino acids and reducing sugars. The two processes can happen together, but they are different processes. They are both forms of non-enzymatic browning.