Continuous Effect Monsters::: Jinzo is an example of this, or, the first effect of Raiou. Becomes active when summoned. Does not start a chain. Example: "Spirit Reaper (cannot be destroyed by battle effect).
Ignition Effect Monsters::: One example is Snipe Hunter. Remember when you call "pri?" Yeah, that's for Ignition monsters. These effects can be activated as soon as the monster is summoned and reaches the field. Can be activated during M1 or M2. Example: "Exiled Force"
Trigger Effect Monsters::: Activate when a certain condition is fulfilled, such as being destroyed by battle for recruiters, or being summoned for monarchs. Optional trigger effects when chained to one another (2x Mystic Tomatos battling in atk mode) turn players effect is chain 1 then other player's is chain 2. therefore, the non-turn player activates their optional trigger effect. Mandatory or Compulsory trigger effects must be activated. If two Mandatories are chained, the same thing applies for them as for 2 optionals. If Mandatory and Optional occur at the same time, then Mandatory becomes chain 1 and optional becomes chain 2. Example: "E-hero Stratos."
Flip Effect Monsters::: Occur when the monster is flipped face up due to a card effect or damage calculation. If a Flip effect monster would be destroyed in battle the monster is destroyed first, then the effect activates and resolves in the Damage Step (so it can't target itself). Example: "Man-Eater Bug"
Quick Effects::: The only Spell Speed 2 Monster Card effects. Can be activated during your turn and your opponent's turn. One example is "Horus the Black Flame Dragon LV8".