The designator descendants describes all direct and indirect children of the current note - i.e. all those for whom the current note is an ancestor.
The previous syntax of 'descendant' is now deprecated. For post v4 group-based action operators it seems the misspelling of 'descendent' is supported - this is also deprecated usage.
Designators don't allow offset references as with attributes. Thus $Name("Some note") works but children("Some note") doesn't. If an offset designator is needed use find() instead.