When triangles are similar, they could be congruent. However, they do not have to be congruent in order to be similar. So I guess the answer is not always.
When triangles are similar, their angles are the same. But that does not mean that they have to be congruent. They can have the same angles but have sides of different lengths. So you can have two triangles where the angles are the same but where one has sides that are all 3 times the length of the other, for example. In such a case, the two triangles would be similar but not congruent.