If you search for several words, by default there is a boolean AND between them. If you just search for “item a item b”, as a result you will get only the nodes that contain both items.
In the structure you show above, no node contain both item a and item b, so if you search for “item a item b” you will get zero result.
If you want results to show all the nodes that contain either item a or item b, you will need to search for “item a OR item b”