Does sponsoring a child abandoned by their parents suffice in place of sponsoring an orphan?

The reward for sponsoring an orphan is exclusively for those who sponsor an orphan. Sponsoring non-orphans falls under other categories of good deeds, such as "charity, feeding the needy, and covering a Muslim woman." If you spent on a girl, believing her to be an orphan, we hope that Allah will reward you with the recompense of one who sponsored an orphan, for "the intention of the one giving charity, if it is righteous, his charity is accepted, even if it does not reach its intended recipient." Also, "a sincere intention can elevate a servant to the status of one who performed a deed, even if he did not perform it."