The popover and dialog displayed by FacetFilter contain a sap.m.SearchField control. This enables the user to search for specific items in the list.
FacetFilterList internally handles the search and liveChange events by filtering the underlying data model: The search only works when the FacetFilterList items aggregation is bound to a model.
If you enable the liveSearch property of the FacetFilter control, keep the performance in mind as this will result in a backend request for each search character typed by the user.