Classifications There are several different properties that define a monster. Below is a list of them with a brief description of each one.
The Guild is a general class of monster including Impulse, Covert, Psycho, and Cypher. It is a property used in the formation of combos and as the target of skills. While the guild does not directly affect stats the three primary guilds are each generally strong in a respective stat; Impulse with Attack, Covert with Health, and Psycho with Defense. Cypher, unlike Dark Summoner, is considered a fourth guild and can't be used to complete a guild combo in Dark Rebirth. Cypher also doesn't seem to have a notable stat sway, with each cypher usually having a different prime stat(s).
A letter describing the general strength and rarity of a monster. Each has a different maximum level.
Simply what the monster is called. There is no strategic use of this property. Unlike other properties, repetition of monsters with the same name/ID will disqualify you from combos rather that build them. However, a '+' version of a monster is counted seperately from a normal version of a monster. I.E: Spotted Cait Sith and Spotted Cait Sith+ are counted as seperate species, not the same monster due to one being +.
The ability to deal damage in combat, with the higher attack stat meaning higher damage per hit. Attack can be bypassed by certain skills that do set damage like Frozen Blade.
The ability to reduce damage taken in combat, more defense meaning less damage from being attacked. Defense can be bypassed by certain skills that do fixed damage like Frozen Blade.
The threshold of damage to receive before a monster falls. If health falls to 0, the monster can no longer participate in battle. Health can be regenerated with the skills Health,Bandage,Rejuvinate, and Revive. It can also be recovered over 1 turn by using the 'rest' command, or by using a revival potion after a lost fight.
The cost of using a monster. You may only place monsters in a formation if their net BP cost is less than your max. When attacking, the net BP cost of your formation is subtracted from your current BP. It seems that when sacrificing, the amount of BP a monster has when it is being sacrificed seems to have an influence on how many levels the base is raised by.
A physical description of monsters. Includes Beast, Brute, Crawler, Creation, Demon, Mystic, Undead and Wyrm. These are used for combos and for skill targeting, such with the skill Wyrm Bind which targets Wyrm species only.
One of various effects used in combat. Can be used to build combos but many skills will only be used once even if multiple monsters are using it. In Dark Rebirth, two types of skills exist. Passive skills are automatically activated at the start of your first battle in a quest, or during a PVP Battle. Active skills are player activated and require a player to tap on a monster's icon, then tap on the active skill, with exceptions to PVP, where active skills are randomly activated without the player's controlling. Skills can only be used once in a quest, with the exception of revival via Revival Potion or the skill revive, where active skills can be activated again.
A miscellaneous trait used for combos in Dark Summoner. However, this seems to be absent in Dark Rebirth, as no 'Winged Monster Combo' or 'Dark Lord combo' appears, even if under the correct circumstances as Dark Summoner.