No they have to have a polygon as a base.
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Their base shape. For example a rectangular prism has base that is a rectangle. Guess what kind of base shape a triangular prism has? yes, triangle.
The base is different. A rect. pyramid has a rectangle as a base. Because the sides are different length for a rectangle, the triangles will not all be congruent (equal). A square pyramid has a square as the base. All sides of the square are the same length, so all the triangular sides of the pyramid will be congruent.
A square can be a rectangle because a rectangle just has to have four sides and they all have to have right angles, which a square does. But a rectangle can never be a square because a square HAS to have ALL EVEN sides with all right angles. A rectangle possibly could not have all even sides.
A square is a special case of a rectangle. Every square is a rectangle, but not every rectangle is a square. A square is a rectangle with four sides that are all equal in length.
For a start, a square IS a rectangle, so it has ALL the properties of a rectangle. A square has the additional property that all of its sides have the same length.