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. MindTools' Brainstorming page has tools and more information about brainstorming.
A mind map is a visual representation of your issue or topic. It is a tool which is used to visualize ideas and opportunities for broadening or narrowing down search topics. MindTools' Mind Mapping page has tools and more information on mind mapping.
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" on the Credo Reference homepage):