I have been working as a software consultant for more than 11 years. Because of that I am an eager supporter of lean principles and agile methods.
While continuous integration triggers a build and automated tests as soon as anyone checks in or integrates the latest code changes, it is still needed to check in frequently to stay out of integration problems.
Continuos testing however runs the automatic tests continuously in the background as soon as the individual developer compiles his code. This way the developer gets immediate feedback both on compiler errors as well as regression test errors and the time and energy to keep the code well tested is reduced.
Read more:
Continuous Testing - research and an Eclipse plugin for continuous testing.
Continuous testing and CruiseControl - article by David Saff, developer of the plugin