CODE EXAMPLE FOR SQL

are both the inserted and deleted tables used in update trigger

Yes. 

ex (table is empty to begin with)

INSERT INTO [dbo].[test_employee_table](letter)
values('a'),('b')

-inserted table count: 2
-deleted table count: 0

update [test_employee_table]
set letter = 'b' where letter = 'a'

-inserted table count: 1
-deleted table count: 1

delete from [test_employee_table]
where letter = 'b'

-inserted table count: 0
-deleted table count: 2