The events to which DML triggers can respond are: UPDATE, INSERT, DELETE.
A DML trigger may also cause any of these 'events' to occur, too, if it performs UPDATE, INSERT or DELETE operations - though these may not be caught, either by the trigger itself or by other triggers, depending on your settings for nested triggers and recursive triggers.
DDL triggers in v9 respond to different events, but similar consideration apply.
I'm not sure from your post if this is the info you need.
Tim Wilkinson
"If it doesn't work in practice, you're using the wrong theory"
- Immanuel Kant