Prisms have polygonal cross sections and several rectangular lateral faces. Cylinders have circular cross sections and one curved lateral face.
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Prisms have polygons as bases whereas cylinders have circles as bases. In a way, a cylinder is like a circular prism.
Alike: Both Cylinder and Prism have the same corresponding Top and Bottom. This is the definition. A Cylinder can be considered as a prism with infinite no. of sides. Different: The side walls of any Prism are flat but that of a cylinder is curved.
... whereas one of the "bases" of prisms are vertices.
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.