I believe there is no strict rule for how to distinguish between monsters and animals, beyond those you already suggested. While you can pick freely which characteristics distinguish them, I’d suggest tailoring them to your world. They should mean something. Perhaps monsters are magical to show off the magical system/ideas of your world. Perhaps they are tormented souls of humans to show how grim your setting is. You might make monsters more intelligent to help people emphasizing with them, or blur the line completely by just making monsters a fictional kind of animal to support a scientific narrative.