Thinking is still currently unique to living things, so you don't need to resort to what you describe to find the human brain uniquness.
Onto what you describe, it has to do with memory. Memory is storing and playing back sensory input, in the absence of that sensory input. So your brain plays back some past sensory input and checks it against current sensory input.
Eg you left the pen on the table. When you come back the pen isn't there. Your brain compares the stored memory of seeing the pen on the table vs what you see now.
Onto what you describe, it has to do with memory. Memory is storing and playing back sensory input, in the absence of that sensory input. So your brain plays back some past sensory input and checks it against current sensory input.
Eg you left the pen on the table. When you come back the pen isn't there. Your brain compares the stored memory of seeing the pen on the table vs what you see now.