Type 1: trying to solve a specific problem. You need to get a heavy canoe down a cliff. You need to design a boat that can be packed into a rucksack. You need to extricate a stuck vehicle from deep sand.
In these type of problems we know our desired outcome very well. We can visualise the ENDPOINT but not the startpoint. For this type of problem brainstorming is useless. What you need is spiral thinking (see the entry by that name) plus, sleeping on it. By spiralling the situation you are simply circling the thing, checking everything out, seeing what is there, observing and not deciding anything. You may come in closer and closer, zooming in as you see what is needed but nothing is forced. You are loading the brain with all it needs to solve the problem. You wake in the morning and hey presto it is solved.
Type 2: This is the open ended type of problem typified by coming up with a GREAT advertising slogan or campaign. Brainstorming was designed for this and works admirably. How many uses can you think for a brick? Brainstorm it and you’ll think of hundreds. There is no fixed ENDPOINT apart from coming up with a GREAT idea. So you need to just chuck as much mud at the wall as you can. You can use this to come up with characters and plot situations too.