There are some effects that take place after a character is destroyed (i.e. loosing the Fellowship of the Ring attachment). Is this the same as discard a character, like Escort from Edoras or Galadriel who are discarded? Is it like they are destroyed or it is different thus the "destroyed effect" does not occur?

destroyed != discarded .... so if an effect take place after a character is destroyed, it will not take place after a character is discarded.

Destroyed is only when they leave play by taking damage equal to their hit points. Discarding them is different and will not trigger effects that happen when a character is destroyed.