A backing bean is a bean that backs JSF Views. In other words, any bean that's directly referenced on a JSF view definition.
In order to make sure that the backing bean is actually going to exist when the view is realized, it has to be a managed bean, so that the system will know what kind of bean to construct and what symbol name to reference it by.
For the most part, managed beans and backing beans are one and the same. But they're all POJO's at heart, just constructed by the JSF framework instead of some other mechanism.
An IDE is no substitute for an Intelligent Developer.