Mysql: does full-text cover normal index?
No.

(Is that answer short enough and decisive enough?)

A regular index can be used for these, yet a FULLTEXT index cannot:

WHERE price = 12.34  -- numeric comparison
WHERE quantity &gt; 100  -- not "equality"
WHERE country_code = 'US'  -- possibly to short for FULLTEXT
WHERE col LIKE '% foo %'  -- note explicit check for spaces
WHERE col LIKE '%=%'  -- punctuation


But for searching for a "word" inside a "text" column, FULLTEXT is excellent.  You have to live within its limitations.