One of the Shub-Niggurath mysteries calls for action after a monster is defeated. Does this include when you discard a monster from a Tokyo encounter or kill it from inducing a loss of health from Tokyo? With no further clarification on the wording, I would think discarding an entire monster would be considered defeating it as it gets blasted from the Earth.
Page 8 of the Reference Guide
When a Monster has lost Health equal to or greater than its toughness, it is defeated.
When a Monster is defeated or discarded, it is returned to the Monster cup and the cup is randomized.
If you have to encounter something (such as an ambush) on a temporary basis and are able to do enough damage to it in one go to kill it, then it is considered 'defeated'. However, it does make a distinction here about both 'defeated' and 'discarded'. This means that, as far as I can tell, there is a precedence about the difference between the two. So, no, discarding does not equal defeated.