primary key vs unique not null

example.sql

create table unique_test (
  id serial primary key,
  u integer unique not null, text text
);
insert into unique_test select i as u, i as text
from generate_series(7, 10007) as i;

# explain verbose select u, text from unique_test group by id;
                                  QUERY PLAN                                   
-------------------------------------------------------------------------------
 HashAggregate  (cost=170.01..270.02 rows=10001 width=40)
   Output: u, text, id
   Group Key: unique_test.id
   ->  Seq Scan on public.unique_test  (cost=0.00..145.01 rows=10001 width=40)
         Output: id, u, text
(5 rows)

# explain verbose select u, text from unique_test group by u, text;
                                  QUERY PLAN                                   
-------------------------------------------------------------------------------
 HashAggregate  (cost=195.01..295.02 rows=10001 width=36)
   Output: u, text
   Group Key: unique_test.u, unique_test.text
   ->  Seq Scan on public.unique_test  (cost=0.00..145.01 rows=10001 width=36)
         Output: id, u, text
(5 rows)