People and scientists both solve problems in the same way. They both use the steps of the scientific method. Non-scientists may not think that they use the steps of the scientific method, but they absolutely do. The steps of the scientific method are as follows:
- Make an observation
- Ask a question
- Create hypothesis
- Test the hypothesis
- Collect and interpret data
Scientists for sure use those steps, but how about a kid playing a video game?
- My character just died. He was killed by that crazy hard boss. (observation)
- How can I beat that boss? (question)
- If I use a different, more powerful weapon, I can defeat the boss. (hypothesis; it's a testable predictive statement)
- Try the boss fight again with a different weapon. (test)
- It worked! (data interpretation)
- This weapon is amazing, and I can defeat more bosses with it. (conclusion)
I use the scientific method all of the time. I was working on my Jeep two days ago, and I was trying to track down an electrical issue with the interior lights. I observed that the dome light didn't light. I figured it was a bad bulb. A new bulb didn't fix the problem. New hypothesis = short in the system. I tested that, and found out that the light does indeed light, so there is no short. It turned out that the problem was that the jamb switch was bad and didn't make a good ground connection any more. I have to replace the part (next weekend). I wasn't intentionally using the scientific method, but I absolutely was using those steps to solve my car problem.
I would say that the only difference between scientists and non-scientists for problem solving is that scientists tend to be very deliberate in their use of the steps of the scientific method.