Your friend has the correct definition. In this case there is without question a correct definition, largely because it is universally accepted definition in the queer community.
Coming out: Admitting you are queer (Gay, Lesbian, Bi, or Transgender) to a loved one, friend, workplace, co-worker or society in general.
Going full time is not coming out. That is why it is described as the real life test or going full time.
Coming out is telling your friends, family and co-workers about who you are. It is a process that anybody who is queer may have to face, even though some never do.
I came out to both my family, many of my friends, and my place of employment. All for different reasons. I am nowhere close to going full time. But to those people important in my life I am out of the closet.