Jag skulle vara nyfiken på om en LEFT JOIN till en motsvarande CONTAINSTABLE skulle fungera bättre. Något i stil med:
SELECT a.CollectionID
FROM collections a
INNER JOIN determinations b ON a.CollectionID = b.CollectionID
LEFT JOIN CONTAINSTABLE(a, *, '"*fa*"') ct1 on a.CollectionID = ct1.[Key]
LEFT JOIN CONTAINSTABLE(b, *, '"*fa*"') ct2 on b.CollectionID = ct2.[Key]
WHERE a.CollrTeam_Text LIKE '%fa%'
OR ct1.[Key] IS NOT NULL
OR ct2.[Key] IS NOT NULL