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)