What's the difference between a cursor and a trigger?
Generally, a cursor is used to iterate through a result set that was returned by a SELECT statement. 

Cursors can be used in stored procedures, stored functions, and triggers. 

A trigger is a stored program executed automatically to respond to a specific event like an insert, update, or delete. 

As you can see, these are very different concepts and have very different purposes. 

I suggest you review these links for the basics on both of these concepts: 
Triggers, Cursors