You will have to unnest the elements then apply an EXCEPT clause on the "unnested" rows and aggregate back:
select col1,
col2,
(select string_agg(item,',' order by item)
from (
select *
from string_to_table(col1, ',') as c1(item)
except
select *
from string_to_table(col2, ',') as c2(item)
) t)
from the_table;
I wouldn't store that result in a separate column, but if you really need to introduce even more problems by storing another comma separated list.
update the_table
set col3 = (select string_agg(item,',' order by item)
from (
select *
from string_to_table(col1, ',') as c1(item)
except
select *
from string_to_table(col2, ',') as c2(item)
) t)
;
string_to_table() requires Postgres 14 or newer. If you are using an older version, you need to use unnest(string_to_array(col1, ',')) instead
If you need that a lot, consider creating a function:
create function remove_items(p_one text, p_other text)
returns text
as
$$
select string_agg(item,',' order by item)
from (
select *
from string_to_table(col1, ',') as c1(item)
except
select *
from string_to_table(col2, ',') as c2(item)
) t;
$$
language sql
immutable;
Then the above can be simplified to:
select col1, col2, remove_items(col1, col2)
from the_table;