The two types of solids are amorphous and crystalline solid!
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Spheres
Those would be called similar solids.
cone
The intersection of two or more solids can either be an empty set, a point (two cones "intersecting" apex-to-apex), a line (two cubes touching along one edge), a face (two cubes, face-to-face). If the solids are "filled", the overlapping intersection will be another solid. If they are hollow, it will be a closed three dimensional figure.
People think about a cylinder as closed, and so the solids, or faces, that it has are on the bottom and top. Those two circles are the only faces in a cylinder. Examples: a soup can, some types of jars, candles (some).