Does this mean I'm becomming a Public?

I'm still "backfilling" content from my paper journal into this blog and as I was typing one up today I had an odd memory from my kindergarten days. I was attending a local Catholic School and had several friends in a Public School. So, using the little bit of logic I had at that young age I assumed that they were "Publics" ... if Catholics go to Catholic School... when you go to Public School you must be a Public.
So the question is ... now that I'm heading down this path... Am I becoming a public?