E
Bar and Baz differ by only one letter, whereas Foo differs from both Bar and Baz by all 3 letters.
So it makes sense that when checking the similarity of random 2-word permutations, swapping Bar and Baz shouldn't make a big difference, whereas swapping Foo with one or Bar or Baz should make a big difference since Foo doesn't share any common letter with these words.
This is why in your results, the 4 permutations that include Foo have a stronger similarity with Foo Bar Baz than the 2 others that don't include Foo.
It should be noted that pg_trm does not care about word boundaries.
As they are lined up, the examples provided in the question could make you believe that a similarity of 0.8 means that one 3-letter word out of 3 is missing, but that's not how it works with trigrams.
This query might help to visualize how strings 1-4 are closer to Foo Bar Baz than strings 5-6:
with l(term) as (values
('Foo Bar Baz') -- reference
('Foo Bar'), -- your examples
('Bar Foo'),
('Foo Baz'),
('Baz Foo'),
('Bar Baz'),
('Baz Bar')
)
select term,show_trgm(term) from l;
Result:
term | show_trgm
-------------+---------------------------------------------------------
Foo Bar Baz | {" b"," f"," ba"," fo","ar ","az ",bar,baz,foo,"oo "}
Foo Bar | {" b"," f"," ba"," fo","ar ",bar,foo,"oo "}
Bar Foo | {" b"," f"," ba"," fo","ar ",bar,foo,"oo "}
Foo Baz | {" b"," f"," ba"," fo","az ",baz,foo,"oo "}
Baz Foo | {" b"," f"," ba"," fo","az ",baz,foo,"oo "}
Bar Baz | {" b"," ba","ar ","az ",bar,baz}
Baz Bar | {" b"," ba","ar ","az ",bar,baz}
