There is a further sub-division of Monsters as to whether they have intelligence and whether they have a humanoid form.
Demonic Being (魔族 mazoku, lit. "Demonic Tribe") refers to Monsters with intelligence with whom it's possible to communicate with.
Majin (魔人 majin, lit. "Demonic Person") refers to Monsters with a humanoid form.
There are different types of Monsters.
Material Monsters are Monsters that have been born with a material body within the material plane.
Spawned Monster are those who have been formed from a cloud of Magicules. This type of monsters usually spawn in areas with extremely high magicule concentration, the higher the concentration, the stronger the resulting monsters end up being. For these reasons, monsters of this type usually appear in Dens of powerful monsters, or in places where a True Dragon resides, like Jura Forest, where Veldora's presence turned the entire forest into a danger zone. The Spawned Monsters are usually material, however, there can be rare exceptions where Spawned Monsters can be born as Spiritual Monsters as well.
Mutated Animals are Monsters that were formerly normal animals who mutated due to running into areas with high magicule concentration. It should be noted though that normally animals are negatively affected by Magicules and would likely even die from the toxic radiation in most cases, but in some cases, the body adapts instead and causes the animal to turn into a Monster that can handle magicules to a certain degree. There are also cases where someone intentionally creates such Mutated Animals via experiments.
There are cases where Humans change into races of Majin via various methods. They could replace their human heart by a magical one, to have a gathering spot for Magicules like Myulan, detach their Spiritual and Astral Body from their Material one and possess the more Magicule-receptive bodies of Majin and Otherworlders, like Razen, or modify your body in some other way like Leon Cromwell did to become a Demonoid. Otherworlders, despite sometimes being able to carry magicules in their bodies, are usually not considered as Monsters, though there are special cases like Razen.
Daemons that have gained a body are for all intents and purposes Material Monsters, and depending on the quality of the body and the summoner's offering, can maintain their bodies for a long time or even permanently. It should be noted that destroying an Incarnated Daemon doesn't kill them, but instead only causes them to revert to a full Spiritual Being that then gets ejected back to the Spiritual Plane.
Semi-Spiritual Monsters are Monsters that are in-between material and immaterial existences.
Some monsters that have been born within exceptionally high magicule concentration might mutate toward being more spiritual in nature. For example, the Monsters within the tunnels of the Sealed Cave, whose bodies have transformed to be less biological and contain no blood, some, like the Tempest Serpent nearest to Veldora's cave, even increased in terms of Magicule capacity, in case of the Tempest Serpent from A-minus to full-fledged A.
Evolved Semi-Spiritual Species
Some evolved monster species naturally become Semi-Spiritual Monsters. That's the case for the Oni, especially Dark Oni like Shion.
Spiritual Monsters are Monsters that are able to exist and operate entirely without a Material Body, though it should be noted that Spiritual Beings, in general, are divided into those who can exist within the Material Plane without a Material Body, and those who can't and instead get ejected back to the Spiritual Plane.
Spawned Spiritual Monsters
There are monsters that get spawned as Spiritual Monsters in the Material Plane with differing strengths. Charybdis is one of them and can exist in Spiritual form on the material plane, but needs a body to possess to be able to operate properly and lacks intelligence. It's unknown how many of those traits other Spawned Spiritual Monsters share with Charybdis.
Daemons are Magicule-based beings, so they are also considered as Monsters. They are among those Spiritual Beings that cannot exist within the Material Plane for long, just like Spirits. Daemons usually gain a body through the contract with the one who summoned them to the Material Plane, which is either the summoner offering their own body and soul, someone else's body and soul, or some other compensation.
Evolved Spiritual Species
Some evolved monster species naturally become Spiritual Monsters. That's usually the case with True Demon Lords. They don't have any of the restrictions other Spiritual Beings have and can switch between Material and Spiritual form at will.
Sometimes Monsters spontaneously develop differently from their kin. They might be a stronger sub-species, be born with additional Skills or have certain traits. The Orc Disaster Geld was one such existence, who was born with the Self-Regeneration Skill.