The Menger sponge is a fractal. It is a cube built up by smaller cubes and where a regular pattern of smaller cubes are removed. Each face of the sponge is a Sierpinski carpet, which is why the Menger sponge is sometimes also called a Sierpinski sponge. At each recursion step, the cubes with an edge on the edge of the larger cube from the previous iteration are kept.
A Sierpinski-Menger snowflake is a variation to the Menger sponge. It is also a cube-based fractal but now eight corner cubes and the central cube are kept at each recursion step. This fractal can be thought of as a 3D analog of the Vicsek fractal.