The term Banish is used in special cases when enemies are removed without being Destroyed, usually because players with enemies On Deck Visit a Port. When enemies are Banished, the Enemy Agenda is advanced as many steps are there are remaining health points for each Banished enemy.
For example, if an enemy with a printed health value of 5 but with 2 Trauma is Banished, the Enemy Agenda is advanced 3 (5 minus 2) steps. Then the enemy is removed.
The Enemy Card for the defeated enemy is put in the enemy card discard pile, unless some game effect says to do something else with it. (Enemy ship cards may be more practical to keep in a separate discard pile, though.)
Destroy
The term Destroy is used to refer to enemies and Crew members that are defeated and removed from the game (possibly to respawn later). The term Destroy is contrasted against Banish, which is something which happens when enemies are removed without being Destroyed.
The term Destroy(ed) is also used when Nodes on a player's Ship Board become disabled due to damage, typically from enemy ship attacks. Destroyed Nodes can be repaired using the Repair Service when you Visit a Port.