Gill fungi have gills under their caps -- the thin, vertical items beneath the reddish mushroom cap shown at the left. In most side views of mushroom caps you can't see the gills as nicely as in the photo, but here a critter has nibbled the cap's rim so that it no longer folds over the gills, hiding them. Gills radiate from a mushroom's stem, is better see in photos below. Millions of spores are produced on these gills. The spores fall downward and then are spread elsewhere by the wind.
The "classic" gill fungus has an open-umbrella shape, and a "classic" mushroom is shown at the right. That's the deadly poisonous Amanita verna, one of several mushrooms going by the quaint name of "Destroying Angel." Only a few gilled mushroom species possess both the ring (also called the annulus) and the cup (also called the volva). Sometimes a mushroom species arises from a cup but has no ring; sometimes it has a ring, but no cup, and; often it bears neither ring nor cup.
The gilled mushrooms are among the most important fungi not only because they are so common, but also because they provide some the best fungi to eat. For example, the mushroom at the right is a member of the genus Lactarius. Members of this genus are often called Milk Mushrooms because when they are injured the fungus body "bleeds" a white latex or "milk," as shown by the cut across the gills in the photograph. In this species injured tissue turns brown, as the image also shows. The "milk" and brown bruises are good fieldmarks, and that's good, because many Lactarius species are wonderful to eat, and these fieldmarks help us identify them..
The little fungus at the right, about an inch across (2.5 cm), is gilled, grows directly upon dead wood without a stem, and thus is not at all "mushroom shaped." It's an abundant species throughout much of North America, often found on dead twigs fallen onto the forest floor. I can't find a common name for it. It's Schizophyllum commune, and if you study experimental genetics you may use this species a lot because it is famous for fruiting readily in culture in the laboratory.