Maddening Dilemma - Compare each cell within column a to each cell in column b and find unique matches

I have been trying to find a way in which i can have excel search
through two columns to find each unique match between the columns and
somehow change the formatting (like highlighting) to fish out the
matches. The problem is that i cannot think of a way to get each cell
in column a compared to each cell in column b, rinse and repeat for
the entire column a. And i am talking about thousands of rows per
column, and the columns are not necessarily the same size. Maddening!

If anyone has any ideas that do not involve installing shareware
plugins, please let me know!

Thanks!