Well they are different shapes:
prism:
A solid object that has two identical ends and all flat sides.
The cross section is the same all along its length.
The shape of the ends give the prism a name, such as "triangular prism"
It is also a polyhedron.
Pyramid:
A solid object where:
The base is a polygon (a straight-sided shape)
The sides are triangles which meet at the top (the apex).
It is a polyhedron.
This is a square pyramid, but there are also triangular pyramids, pentagonal pyramids, and so on.
Difference:
In a pyramid there are 4 faces which are triangular in shape and there is 1 face which is a square which is its base. On the other hand, A prism has 3 rectangular faces and 2 equilateral triangular faces which work as its base.
Similarity:
Both of them have triangular faces. Actually I don't find any similarity between them, except that and they are polyhedrons. Plus the base of a pyramid alters the name of the pyramid, just like the end of a prism does.
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