The Vision describes the way you see your organization, your research group or yourself after you have reached your goals; it is the optimal desired state in the future, say 5-10 years away from now. You could also call it a dream, but it should be a realistic one. The scheme below lists a number of questions which will help you to formulate a Vision for your research group (your unit) in relation to the organization it belongs to, as well as for you personally. Your team members may use the right part of the scheme to develop a personal vision for themselves once you can present them your views for the research group.
"Good leaders create a vision, articulate the vision, passionately own the vision, and relentlessly drive it to completion."
- Jack Welch, CEO General Electric.
The Mission describes the present purpose of your organization; it specifies what is does, for whom and how, and with a focus on a shorter term from now till 2-3 years from now.
Vision and Mission together contain a clear description of what you want to achieve. It may be that your coworkers or students are more interested in your mission statement, as it has immediate impact on their activities now. However, the organization you belong to, including your Head of Department of even the Executive Level of your university of research institute will have a keen interest in both, and especially where you want to go in the long run.