MySQLで優先度を使用して複数の列を検索するにはどうすればよいですか？

それは解決策の1つである可能性があります：

SELECT id, desc, abbreviation, etc FROM
( 
   SELECT 1 AS rnk,  id, title as 'desc' , abbreviation , etc FROM shows 
   WHERE abbreviation LIKE '%".$term."%'
   UNION 
   SELECT 2 AS rnk,  id, title as 'desc' , abbreviation , etc FROM shows 
   WHERE title LIKE '%".$term."%' 
) tab
ORDER BY rnk
LIMIT 10;

または、次の方法で同じことを実現できます：

SELECT  id, desc, abbreviation, etc FROM
(
    SELECT CASE WHEN abbreviation LIKE '%".$term."%' THEN 1 ELSE 2 END As rnk,
    id, title AS desc, abbreviation, etc 
    FROM shows 
    WHERE abbreviation LIKE '%".$term."%' 
    OR title LIKE '%".$term."%' 
) tab
 ORDER BY rnk
 LIMIT 10;