I've seen 是的 used multiple times as a "yes" answer to a question.
As in the following interaction:
How is it different than just 是 by itself?
是的 is the formal usage, while
是 is informal, and short. And
是的 has the self-sufficient feel, as if it had a period attached to it, while
是, on the other hand, feels like it has a comma attached, inviting both sides to expand on it. For example: