The difference is the shape. A cube is a 3D square. A square pyramid is a pyramid with for sides and a square on the bottom.
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Square is to cube, as triangle is to "triangular pyramid." Pyramid might refer to the common square pyramid, with a square base.
Pyramid
The square based pyramid does not stack or roll.
Cube and pyramid
A square prism is shaped like a cubid. A square pyramid is a pyramid with a square base.