What's a mulberry?

Hunter and I have begun the routine of exploring our "yard" by hiking either early morning or evening. Our current location, at a campground in Rock Island, is surrounded on three sides by bodies of water, off shoots of the Mississippi and small roads leading to other seasonal camper spots. One evening, while on our trek, I noticed trees loaded with small dark berries. My "walking encyclopedia" husband immediately identified them as mulberries. That night we picked and ate our fill from several trees. Being an incessant baker I wondered about the possibility of harvesting those berries for a pie.
The following day I did some internet investigation and learned that this fruit was not really a berry but a collective fruit and only resembled a blackberry in appearance. The trees in Rock Island are white mulberry trees, rather than black ones. I only know this because they produce their fruit in spring instead of summer or early fall. Even though they bear the name "white" they can produce white, lavender, or black fruit. Locally the trees bear black fruit, which stains your fingers immediately! Since I learned they were suitable for pies, the following evening we gathered a plastic table cloth and set out to harvest dessert. It was fun to shake the branches and watch the fruit fall into piles on the red-checkered cloth. We are talking here about wild fruit, therefore along with the sweet morsels we got a variety of dried leaves, sticks, bugs, and tiny worms. When we returned to our RV we soaked our treasure in a large bowl of cold water hoping the little "critters" would swim to the surface while the berries sank. That didn't work exactly as planned. It took me quite a while to carefully examine the "berries" on the kitchen counter to feel relatively sure they were bug and worm "free".
Today I made the pie and it was truly delicious. I almost feel akin to Daniel Boone's wife! I even baked the pie in my "outdoor" oven!(Check out the picture below.)
Hunter just came back from a little fly fishing in the "backyard" and he said he spotted an elderberry bush. Another pie possibility? I'll let you know.