What is the difference between being depressed and "feeling" depressed?

What is the difference between being schizophrenic and having the "opinion" that Satan speaks to you through your neighbor's cat?

Mental illness is defined by what a person feels and believes.

What you feel and believe is subjective but you can objectively establish that a particular cluster of subjective feelings and beliefs is abnormal vis-a-vis a populate.

Then when you ask people the same questions and their cluster of responses fits the abnormal definition you can objectively say that they have a mental illness.

The objectivity does not come from the doctor observations or patient self-survey, it comes from the study that created the questions and proved that a certain score or cluster of responses is statistically abnormal.