Just that when "native" thinking is used it's hidden from the end result via special tags. If you force a model to reason about a result before producing the result, you get more accurate results.
Because "reason" comes before the selection, it has to think through why it is producing the result beforehand (e.g. produce a block of text that makes the correct answer statistically more likely to be sampled from the distribution. Giving it a property name does influence the direction of the thinking, but it's the same concept. You can call the property "yourThinking" too.
It sounds like you may be thinking too highly/mysteriously about how LLMs work.
At the end of the day they stream completely unstructured text outputs and all behaviors on top of that are just parsing XML-like tags to do tool calls, hide thinking etc (which they were trained to produce in certain circumstances).
There is no special "thinking process" it is a stream of text in the response that is simply wrapped in <Thinking> tags (or similar)