If you are asking if Self-Employment income "counts" for Social Security purposes, YES it does.
So, technically the answer to your statement:
"I understand if you are self employed the income does not count, true or false." is
As far as what is the definition of "self-employed" in the eyes of SS, it is the same definition that is used by the IRS, namely you operate a business as a Sole Proprietor or a Partnership. You are in business for yourself, selling a product or products or performing a service, or making something to be sold on a wholesale or retail basis.
For example, in terms of selling a product(s), you could own & operate a retail establishment, a gift shop, a restaurant or any other retail store. Performing a service could be an attorney, an accountant, a barber, etc., and making something could be making birdhouses, tables, etc.