The best place to start and learn about SOQL, SOSL and Triggers is Apex Basics & Database at trailhead.
SOQL can be used in Triggers but SOSL is not. The idea to allow it has been raised away long back. You can upvote it:- Allow SOSL queries in Triggers
SOSL queries are only supported in Apex classes and anonymous blocks. You cannot use a SOSL query in a trigger.
You can get more information here:- Introduction to SOQL and SOSL