Brainstorming is a way to come up with topics or ideas. It allows a person to casually consider multiple topics, ideas, theories, etc. without judgment and to take some ideas further into actual projects or as tools to consider more topics, ideas, theories, etc. For more information about brainstorming visit MindTool's Brainstorming page.
A mind map is a visual representation of your issue or topic. It is a tool that is used to visualize ideas and opportunities for broadening or narrowing down search topics. For more information on mind mapping visit MindTool's Mind Maps page.
There are a number of free brainstorming and mind mapping tools available online like Bubbl.us and Popplet. Alternatively, try the mind map available via Credo Reference (click "Mind Map" from the drop-down menu beneath "Basic search" to the right of the search box on the Credo Reference homepage):