Question

What are all the moves and abilities that have different effects based on the targets/users/ally's type?

Comments

Curse and (arguably) Revelation Dance are two that immediately come to mind, though there's probably more I'm just forgetting.

If we expand to include items, Black Sludge can be added, too.

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Almost all damaging moves

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effects, not damage.

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damage is an effect, no?

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No, effects are things that have to be specified under the damage it is said to deal, eg Mud Slap does damage, and has an effect, to lower accuracy.
Additionally, even if I'm wrong, I don't think OP was asking for every typed damage dealing move, just ones like Rototiller, Curse, Symbiosis, etc where it has to be specified that it changes.

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nobody?