Praise be to Allah.
The orphan is a child whose father has died, as was stated by the scholars in Lisaan al-‘Arab [an Arabic-language dictionary] and elsewhere. Such a child is regarded as an orphan until he reaches the age of puberty, i.e., the age of fifteen or earlier if the signs of puberty appear. These signs are: the emission of gushing water (ejaculation) during intercourse or a wet-dream, the growth of coarse hair around the private parts, and, in the case of females, the onset of menstruation.(See Al-Mughni by Ibn Qudaamah, 6/591)
As for the child whose father is missing, he is not considered to be an orphan unless it is proven that his father is dead, or a period of time passes beyond which it is impossible that his father would still be alive; this should be left to the discretion of the judge, as stated by the majority of the fuqaha’ on the topic of the inheritance of one who is missing.
If this child is poor or comes from a poor family, then money can be spent on him from the Zakaah or general charity funds, but orphan sponsorship does not apply in his case.