SQL LIKE with no wildcards the same as '='?

I know this is a pretty basic question, and I think I know the answer...but I'd like to confirm.

Are these queries truly equivalent?

SELECT * FROM FOO WHERE BAR LIKE 'X'
SELECT * FROM FOO WHERE BAR ='X'

Perhaps there is a performance overhead in using like with no wild cards?

I have an app that optionally uses LIKE & wild cards. The SP currently does the like and appends the wild cards -- I am thinking of just updating the query to use like but have the app append the wild cards as needed.