They serve very different purposes.
- Full Text Search is used to return documents that match a search query of stemmed words.
- Trigrams give you a method for comparing two strings and determining how similar they look.
Consider the following examples:
SELECT 'cat' % 'cats'; --true
The above returns true because 'cat' is quite similar to 'cats' (as dictated by the pg_trgm limit).
SELECT 'there is a cat with a dog' % 'cats'; --false
The above returns false because % is looking for similarily between the two entire strings, not looking for the word cats within the string.
SELECT to_tsvector('there is a cat with a dog') @@ to_tsquery('cats'); --true
This returns true becauase tsvector transformed the string into a list of stemmed words and ignored a bunch of common words (stop words – like ‘is’ & ‘a’)… then searched for the stemmed version of cats.
It sounds like you want to use trigrams to auto-correct your ts_query but that is not really possible (not in any efficient way anyway). They do not really know a word is misspelt, just how similar it might be to another word. They could be used to search a table of words to try and find similar words, allowing you to implement a “did you mean…” type feature, but this word require maintaining a separate table containing all the words used in your search field.
If you have some commonly misspelt words/phrases that you want the text-index to match you might want to look at Synonym Dictorionaries