Scary Monsters Exist in Every Culture Since the Dawn of Time. Awesome!
Monster horror is a broad subgenre of horror. Capital M Monsters represents the monster itself, which takes many forms in many cultures. It is a capital M because Monsters become a symbol… a symbol that is potent and transformative.
A Monster can broadly be any physical being that enacts some kind of harm to the protagonist. For purposes of classification it is something that is not strictly another human or traditional animal. It could be blended with the Slasher subgenre and be a human that has been endowed with superhuman abilities like Jason Voorhees, or an animal that is not considered conventional like Graboids or giant spiders. A capital M Monster is a villain that is both physically threatening (does not typically rely on magic) and supernatural (abnormal).
Some Monsters have become so popular that they are upgraded to becoming an entire subgenre, such as Vampires and Lycanthropes. Monsters that are animals are filed under Natural horror. Monsters that are human or human-like are typically filed under Slasher horror. But as is always the case, genre is a classification system that involves complexity and often a lot of opinion. Most horror movies blend numerous subgenres.