If I'm correct April said that in the charity-world you can also use the term 'orphan' in terms of 'economic orphan', as a way of saying that a child is orphaned by society.
Having said that, I myself personally only use the term for children that have lost (or abandoned by) their parents.
I understand charity industry may have different definition for "orphan". Since we are not in the industry, we should go by common dictionary definition which is the same as your understanding...
http://www.dictionary.com/browse/orphana child who has lost both parents through death, or, less commonly, one parent.
sadly, I'd also consider an orphan a child whose parent chose to abandon at birth or later in life.