Yes, all of these things are used to identify the mushroom, because the shape of the bell, the stem, etc. all change depending on the growth stage of the mushroom. But sponge is sponge, and gill is gill, and they never change regardless of which stage the mushroom is in.
Because many of the sponge ones are edible, the boletus kind, and turn blue when bruised – these are the safest and there aren’t so many similar kinds that are
poisonous to confuse them with. Whether the gills are attached to the edges of the cap, or stop just prior to reaching it, is another important identification factor in mushrooms.
In Poland, (where I used to live) mushroom picking is THE THING to do, especially in the autumn, when the best kind are available (and dried for use in Bigos, a national dish at Christmastime.) Here is the U.S. there are different kinds that look the same as the European ones, but aren’t, and can kill you. I always flip the mushroom to take a look before picking – in Poland people were always dying in the autumn, because although they had been picking mushrooms all their lives, they still misidentified a batch, and once your liver/kidney shut down, you die, there is no recovery.
Mushrooms kill – who was it that died in France when he and his friends cooked some mushrooms they had picked? Chopin? I can’t remember off hand, but mushroom picking should only be done with a real expert – I’m still too scared!