The difference between a rectangular prism and a cubic prism is in the equality of the faces of the prism. All sides of a cubic prism are equal, while a rectangular prism's sides have different measurements.
All rectangular prisms are cuboids. The defining factor for a cuboid prism is that it has a total of six faces, and all faces of the prism come together to form 90-degree angles. This means that a cube-shaped prism is a specific type of rectangular prism. The faces on a cube-shaped prism are equilateral, meaning the faces form perfect squares and meet at 90 degree angles.
As the name states, a rectangular prism's faces are rectangles. Two sides of the face are one length while the other two are a different length. None of the faces on a rectangular prism form a perfect square. There is, however, a third kind of rectangular prism, which is the square prism. The defining factor for this specific kind of cuboid is that at least two of the faces are perfect squares, while the other faces of the prism are rectangular in shape. As with the rectangular and cube-shaped prisms, the square prism's faces meet to form 90 degree angles.