As Ashish said, the reasons for awarding a bounty may be different than the reasons for accepting an answer. So let's start with what's obvious: the reason an answer is accepted is usually because it is what solved the problem for the one who asked the question.
Also, as Ashish said, a bounty can be provided by someone other than the one who asked the question. Since there are two separate people involved, there can easily be two different reasons. Perhaps one person just wanted to know what he could do to fix a problem, where as another person might want a more detailed explanation so he can understand the problem more thoroughly.
As a final example, the same person who asked the question may decide to accept an answer because it's the first one that solved his problem, but then out of a desire to understand he may offer a bounty for a more thorough explanation, and end up awarding it to someone else.