The subgenre “Monster horror” consists of any monster movie, show, or story in which the main antagonist of the story is a monster or monsters that prey on the protagonists. It is slightly different than the trope Capital M Monsters merely because a subgenre is meant to describe the entire story, while tropes can exist in many different subgenres. There is a lot of gray area. But for categorizing, it is helpful to separate the monster from a subgenre of horror that is built around a monster. For example, Tremors is a good example of Monster horror with a Capital M Monster. While the Friday the 13th franchise is an example of Slasher horror with a Capital M Monster.
There are also many cases of monsters being in non-Monster horror stories. Arguably the most iconic monster, Frankenstein, is an example of Drama horror. And there are many Children’s horror tales in which the monsters are not the antagonist.
Examples of monster movies in the “Monster horror” subgenre include horror movies of the 1950s like Them! and The Blob to more modern monster films such as The Thing and Sleepwalkers. Many examples of “Monster horror” are combinations of other subgenres, such as Sci-fi horror (when the monster is an alien) or when a monster has become so popular it is its own subgenre (Vampire horror, Werewolf horror, Zombie horror).