A Backing bean is one that's referenced on a JSF View. It provides the backing object for the EL that references properties in it.
A Managed Bean is one that's constructed and initialized by the JSF framework (using the faces-config specifications). Once constructed, it's inserted into the specified scope (request, session, application or one of the new JSF2 scopes).
For almost all intents and purposes, the 2 are identical, since it takes a bit of work to invoke the bean manager directly, and conversely, a Backing Bean is almost always a Managed Bean, since the act of referencing the Backing Bean on a JSF View causes the bean manager to get involved.
Although you could manually create backing beans in a non-JSF servlet/JSP the old-fashioned way and sometimes you even find cases where that's the optimal approach.
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