I see what you are saying and I can replicate what you're seeing. However the two test cases are slightly different.
One difference between my test and yours is that I have a unique primary key. Are they really peers if there's a unique primary key?
Try this:
create table test(a int, b int, constraint a_key primary key (a));
insert into test values (1, 2), (2, 3), (3, 3), (4, 4), (5, 4), (6, 4), (7, 4);
select * from test order by b offset 0 limit 3;
select * from test order by b offset 3 limit 3;
select * from test order by b offset 6 limit 3;
Note the sorting is on b.
A finer break point looking at just 2 records at a time looks like this:
Does having a unique primary key make any difference? Or should it?