1. destitute = utterly lacking; devoid
without means of subsistence, lacking food, clothing and shelter
synonyms: need, poor, penniless
2. abandoned = forsaken or deserted, left alone "an abandoned kitten"
exuberantly enthusiastic , unrestrained and uncontrolled
recklessly unrestrained, free from moral restraint
synonyms: discarded, rejected
As far to your question my humble opinion is: An abandoned child might be a destitute child, but this couldn't be a fact when this child will be adopted from a rich family. Both "abandoned" and "destitute" aren't 100% synonymous expressions. This is only my opinion.
(destitute child - a child who has no sufficient means of subsistence child apparent to the Court and whose near relatives are, in the opinion of the Court, in indigent circumstances and unable to support such child, or are dead, or unknown, or cannot be found, or are out of the jurisdiction, or in the custody of the law.
Abandoned Child [Spouse]Person who has not been in contact with or received support from the parent or spouse. A court finding of child abandonment terminates parental rights and allows the child to be adopted without permission of the parents.