Different search engines, different catalogues, one result in common.
Try this on your own site search:
"X without Y" — X is something you sell, Y is something you don't want
then just "X"
On four of the five sites, the first query returned MORE results than the
second. Not fewer. On three of them, the thing the customer excluded was
promoted to the top of the page.
One site went from 1,340 results to 4,607. The top four hits were all the
excluded term.
Nobody is hiding this. One vendor documents it plainly: if you don't supply
an operator, the default is OR. So "lobster rolls but no Maine" becomes
lobster OR rolls OR but OR no OR Maine. The word your customer used to
exclude something quietly becomes another word to search for.
Which is fine, right up until a customer types a sentence instead of a noun.
Fair disclosure: I build a search plugin, and mine doesn't solve this with a
filter either. It rewrites "without X" into a positive form, which works when
the catalogue has something positive to match and drifts when it doesn't.
Better, not solved.
Run the two queries on your own site. Thirty seconds and you'll know which
kind you have.