What is the difference between "way of thinking" vs "the way they think"

Solution 1:

Way of thinking typically refers to someone's perspective or viewpoint, e.g., "It's a good plan, by my way of thinking."

The way they think uses the definition of way that means "how someone does something," so the phrase would refer to the method or practice that people use to think. For example, the way one person thinks might be by carefully analyzing the facts, while the way another person thinks might be to jump to conclusions.