This mushroom is called amanite, and is quite toxic. Don't eat them!
Some of the patches of woods around us also have names. Closest to us is the Bois des Vaux where Callie and I sometimes walk. She's chased animals in there and that's where we encounter the stuffed clothing nailed to the trees. Spooky. I think that the difference between un bois and une forêt in French is pretty much the same as between woods and forest in English; it's a matter of size, the former being much smaller in area than the latter.
Be they woods or forests, they're not wild places but almost meticulously managed for wood. In forests, paths and roadways are well maintained and hunting blinds can be seen at regular intervals. Forests and woods are refuges for game like deer and wild boar. Except, of course, during hunting season.
Here's a case where an accent mark makes a difference. The word forêt, with the circonflexe over the "e" means forest. Without the circonflexe, it's foret which means drill bit. The words are pronounced exactly alike, your only clue to their difference being their gender: it's une forêt but un foret.