You can do it of course, but I doubt it will be very useful:
select *,levenshtein(lexeme,'color') from things, unnest(to_tsvector('english',description))
order by levenshtein;
id | description | lexeme | positions | weights | levenshtein
----+--------------------+--------+-----------+---------+-------------
3 | Painting colors | color | {2} | {D} | 0
1 | A red coloured car | colour | {3} | {D} | 1
1 | A red coloured car | car | {4} | {D} | 3
1 | A red coloured car | red | {2} | {D} | 5
3 | Painting colors | paint | {1} | {D} | 5
2 | The garden | garden | {2} | {D} | 6
Presumably you would want to embellish the query to apply some cutoff, probably where the cutoff depends on the lengths, and return only the best result for each description assuming it met that cutoff. Doing that should be just routine SQL manipulations.
Perhaps better would be the word similarity operators recently added to pg_trgm.
select *, description <->> 'color' as distance from things order by description <->> 'color';
id | description | distance
----+--------------------+----------
3 | Painting colors | 0.166667
1 | A red coloured car | 0.333333
2 | The garden | 1
Another option would be to find a stemmer or thesaurus which standardizes British/American spellings (I am not aware of one readily available), and then not use fuzzy matching at all. I think this would be best, if you can do it.
