Solo monsters. A fight with this type of monsters always consists of 1 round. Only 1 player can enter the fight, no allies or coven members can be invited to help. Solo monsters can be found on the "Monsters" page under the corresponding tab.
Multiplayer monsters. The most common type of monsters in the game. Several players can fight in a battle with a monster of this type, and the battle itself consists of several rounds. You can summon a monster of this type through the "Monsters" page.
Only multiplayer monsters have different versions of them. There's a basic monster and more powerful versions of it. They have the same picture, but they are different. They have different names, level requirements, rewards and power. You get gems each time you defeat a new version of a monster. For example, when you summon a Troll the game randomly picks a version of the monster to summon. But there are limitations: 1) you can't summon powerful versions of a monster until you defeat the basic version of it 5 times. 2) The higher your level is, the higher chances you have to summon a more powerful version of a monster.
Altar monsters. A monster of this type can only be summoned by a coven, and only coven members can participate in the battle. Covens use altars to summon these monsters. You can summon Bloodlord through the Mansion, Mountain Troll through the Troll Cave, Poisonous Hydra through the Foul Pit, Minotaur Captain through the Maze and Sea Beast through the Cliff, Cerberus through the Hell's Gates.
Rare monsters. This kind of monsters is only available during the "Monster Hunt" event. For example, a Troll Hunt is on. During this event you have a small chance of summoning a Rare Troll instead of a regular one. You can't summon a rare monster of another family during the Troll Hunt. You will know that a monster is rare right away - it will have a different name and look. Rare monsters require the same resources to be summoned and have the same power as the base monster in the family but the rewards for summoning and defeating them are royal!