The word brainstorm involves thought. A brainstorm can be an "Aha!" moment, while brainstorming is the process of trying to think of ideas. People brainstorm when they need a new idea. You can also say you had a brainstorm when a good idea or solution occurred to you. Often, this kind of brainstorm happens when you're not even working on the problem. For example, a scientist might have a brainstorm for a new project in the shower.

Source: Vocabulary.com