Congruent and Similarity are terms used in mathematics. Congruent is referring to two objects having the same size and shape, so much that, when these objects are placed in the space, they will still be the same thing no matter how they set. Similarity, on the other hand, is simply about resemblance and not be necessarily about two objects having the same size. For example, when you draw two shapes of the rectangle, it is possible they might not be of equal size, but the fact remains that they are similar in terms of shape.
While congruent refers to two objects with matching qualities, Similarity does not talk about multiple resemblances, once you are connected in one aspect, you are already similar items. The dictionary meaning for congruent says when two things coincide exactly when superimposed while Similarity means Closeness of appearance to something else.