Creating a good villain and a good monster in your story is not the same thing. I discovered this while writing a story with a terrific monster, but an unsatisfying ending. I realized I was treating the monster too much like a villain. Once I realized it was a monster, and it needed some monster “rules”, did things fall into place.
[Note: Below I am speaking in absolutes, but consider it advice. It’s just easier to write in absolute terms than conditional ones. Also, I use “hero”, but it’s a non-gender specific sense.]

What’s the difference between a monster and villain?

A villain is a person. (At least, it is person-like.) A villain  has consciousness and free will. It has motives, an agenda, and the ability to anticipate. It is the (proactive) hero of its own story.

Jason Voorhees is not so much a villain as a monster. He doesn’t plan or have an agenda, he just reacts.

A monster works on instinct or the laws of nature. It can be an animal (natural or not—a shark, a werewolf, Godzilla), the environment (e.g., tornadoes, a malfunctioning space ship) or even a person stripped of human qualities (e.g., Jason Voorhees). But, like all things in nature, it can learn and adapt.
Lesson: Your monster doesn’t start with a plan. It acts on instinct and, at first, is predictable. But to make your hero sweat, your monster must learn how to fight against the hero while still being animalistic.

A monster must be invoked

A monster just showing up and wreaking havoc can be fun. (A villain, though, has a motive. It is exactly where it wants to be at a precise time for a specific reason.) Think Godzilla, Night of the Living Dead or The Day After Tomorrow.
But having to invoke the monster adds a layer of guilt or responsibility to the story. Think of Pinhead’s puzzlebox (the Lament Configuration) or the Micmac cemetary. In some incarnations, a vampire must be invited into your home. Reckless campers, well aware of the legend of “Camp Blood”, still enter Jason’s domain.
Even Jaws has its invocation—splashing swimmers attract the shark. If the people of Amity had listened to Chief Brody and closed the beaches, the shark would have moved on.
Lesson: Through invocation, a hero deals with the monster and their own guilt. Invocation can also foreshadow how to destroy the monster. In more advanced stories, like Jaws, the hero must convince others that a seemingly harmless (or even necessary) action is the invocation.

The monster must be monstrous

We think of “monstrous” as big. But the origin of the word “monster” comes from the Latin indicating something is wrong with the natural order. That is, monsters stand in contrast to natural biology.

Pinhead is another monster with a very clear way to invoke him. Rather than have a plan, he reacts to those who summon him. He symbolizes unbridled lust, a taboo in our society.

But they also contrast our sense of right and wrong. Monsters are both physically and morally aberrant and abhorrent.
Godzilla—a massive, destructive beast—embodies our guilt (and comeuppance) for reckless nuclear testing. The relentless killer Jason Voorhees—disfigured and massive—was caused by teenage desire. One summons Pinhead in the pursuit of ultimate pleasure. (And don’t forget the original movie’s murder and infidelity.)
Lesson: When creating a monster, focus not only on its physical attributes but what taboo created it, or what taboo it embodies.

The monster reflects the hero’s weakness

A monster pushes your hero to their limits. The hero cannot defeat the monster at the beginning of the story, but grows and learns in order to win.
To push your hero, a monster must embody your hero’s weakness. Is your hero small or weak? The monster must be huge. If your hero has a simplistic outlook, the monster must be clever. Perhaps your hero cop has lived her whole life in the city; she must confront the monster in the depths of the forest.
In The Day After Tomorrow, the young protagonists are untrained for the climate shift, plus they are not in their home city. Jaws has Chief Brody as a former New York City cop with a fear of the water. Also in Jaws, the shark hunter Quint underestimates the shark’s cunning.
Lesson: When creating your hero and monster, find how the monstrous elements—physically and morally—exploit your hero’s limitations.

So, is that it?

No. There will be more about monsters coming in a later post. This next post focus on the hero and how he/she fights back. For now, I hope this helps.