I am sorry if my question is stupid, but I can't figure out the difference between these three.
A small group of people brought together to discuss, investigate, or decide on a particular matter, esp. in the context of business or government.
A group of people constituted as the decision-making body of an organization.
A body of experts providing advice and ideas on specific political or economic problems.
I would say that boards and think tanks are both kinds of panels, although think tanks stop being considered panels when they are no longer "small."
A board is a group responsible for decision making in an organization. A board of directors makes all of the central, high-level managerial decisions for a corporation, for example.
Think tanks don't make decisions. They try to solve problems and will likely have an advisory role to whoever needs to make the decisions.
Panel is also used when a group of people answer questions for a generalized audience. For example, people who answer questions at a convention due to having inside knowledge of the topic are considered members of a panel. The same would go of a panel that answers government questions fielded by a concerned public. However, this definition of panel is not really related to the one you asked about.