Matching Columns

I have 2 columns of company names but they are not written exactly the same, i.e., Column A may say "the State X Co" and Column B may say "State X Company."  How do I match these two columns?  I cannot seem to get the match feature to work or it.  Or, if I cannot match those that are "fuzzy" like this, how do I just match those in column A that are exactly like those in Column B?  Again, match only seems to give me a list of the matching names, not lining Column A matches up with Column B matches.

Thanks for any help.