Eeebuntu and Ubuntu Eee are two different distros with a similar idea: customising Ubuntu for netbooks.
Eeebuntu is more focused upon the EeePC range although to date we have had reports that Eeebuntu works well on the Eee Box, the Acer Aspire One and the Samsung NC10. Other reports are coming in.
Ubuntu Eee intends to be more of a generic netbook distro.
At the moment Eeebuntu is based on Intrepid Ibex 8.10 whereas Ubuntu Eee is still based on 8.04.
Ubuntu Eee is undergoing a rebranding due to legal difficulties with the name and will become Easy Peasy and be based upon Intrepid.