With the news of Oracle pulling the InnoDB engine from MySQL Classic Edition, you now need to use MySQL Community Edition to get InnoDB for free. Oracle doesn't really make it clear what is different between Community Edition and the rest of the product line.
From what I can tell it looks like MySQL Classic Edition is intended as the free version of MySQL for software vendors. The Community Edition is license under the GPL, making it difficult for anyone wanting to embed MySQL in software they want to sell. The description on the MySQL Classic Edition seems to support this:
"ideal embedded database for ISVs, OEMs and VARs"
The enterprise edition has advanced features that the community edition does not have, e.g. transactions.
http://mysql.com/products/enterprise/
http://mysql.com/products/community/