“Apprenticed out” may indeed sometimes have meant being indentured to America, but most of the time it meant being indentured to a master in a trade to learn the trade. In England or wherever.
Orphans were bound to a master to learn a trade, children of the poor were bound to a master as a servant or to learn a trade, on up the line to apprenticeship. One of my seventh great grandfathers was bound as an orphan after his father was killed in an indian attack and his mother disappeared, to learn “arithmetick and blacksmithing.” He ran off before his obligation was complete, and joined the militia to find his brother during the Revolution. Another came through Maryland in the 1600’s and cost of his transport was paid by a tobacco planter, he was basically sought and apprenticed at sixteen, his father was an apothecary in the southwest of England, his uncle was high sheriff of Exeter. The system sounds cruel to modern ears and perhaps it was to some, but it worked.