these two are  SQL concepts

TRigger is  a special type of stored procedure that 
automatically takes effect when the data in a specified
table is modified.
triggers invoked in response to an INSERT,UPDATE OR DELETE 
STATEMENT EXECUTED.
TRIGGERS are used to handle some exceptional conditions
if u r moving data 40 MB into data base,But data base having
only 30 mB free space then the trigger fires automatically
and the entire transaction automativcally roll backs.

Rules:
Rules are database objects used to enforce data integrity.
this object bound to column or userdefined  data types.
to ensure that only valid values are allowed to insert in 
to columns.

so trigger acts automatically nad rollbacks the transaction
when error is occured.

rule is used to enforce data integrity on a column or user 
defined data type.
 
are you clear if you want any clarification please mail to 
me.