a cylinder has to have a circular base because it is a circular prism
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Strictly, if it has a circular base, it is a circular cylinder. Otherwise, it could have an oval base. If the long axis is at right angles (perpendicular) to the plane of the base, then it is a right circular cylinder.
cylinder
A cylinder is not a prism because it has a circular base and therefore requires a different formula to figure out its volume, surface area, etc.
A prism. A prism is named for its base, eg a triangular prism has a triangle for the base. If the base is a circle, the circular prism is called a cylinder.
A cone has a flat circular base