Bring Out the Mushrooms!

The persistent rainstorms of the past two weeks have produced a full crop of mushrooms. Several dozen of the following were clustered around a dogwood tree, in variously-sized clumps. I am not really sure what these are since there are quite a lot of whitish fleshy mushrooms.

There are also several of these cup-shaped mushrooms in another location. Again, I am not absolutely sure of the identity, but it seems like a Common Brown Cup (Peziza badio-confusa).