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... whereas one of the "bases" of prisms are vertices.
Prisms have polygons as bases whereas cylinders have circles as bases. In a way, a cylinder is like a circular prism.
Cylinders are circles pulled out into the third dimension and rectangular prisms are rectangles pulled into the third dimension.
Cylinders and cuboids are types of prisms.
Prisms have polygonal cross sections and several rectangular lateral faces. Cylinders have circular cross sections and one curved lateral face.