distinct vs group by

Should the expressions
  select distinct x from t
and 
  select          x from t group by x
have the same effect?  

It seems the optimizer sometimes chooses different plans for those
expressions.   Could the select distinct have used the slightly
faster hash aggregate?

   Thanks.



fli=# explain select distinct zip from sa_zips;
                             QUERY PLAN
--------------------------------------------------------------------
 Unique  (cost=3.65..3.98 rows=66 width=8)
   ->  Sort  (cost=3.65..3.82 rows=66 width=8)
         Sort Key: zip
         ->  Seq Scan on sa_zips  (cost=0.00..1.66 rows=66 width=8)
(4 rows)



fli=# explain select zip from sa_zips group by zip;
                          QUERY PLAN
--------------------------------------------------------------
 HashAggregate  (cost=1.82..1.82 rows=66 width=8)
   ->  Seq Scan on sa_zips  (cost=0.00..1.66 rows=66 width=8)
(2 rows)