Ages in records
14 - At 14, free people of either gender could witness documents, such as deeds or wills. At 14, they could also choose their own guardian; before age 14, one would be appointed by the courts. A record of a person choosing their own guardian proves they were over 14, but under 21.
16 - At 16, free white males were considered tithable, and had to pay a tithe or poll tax. Laws varied over time about the ages and genders of free blacks and slaves to be considered tithable. Free white women were never tithable.
21 - At 21, a person attained their majority, or adulthood. Before 21, people were considered minors or "infants" in court records. A head of household was usually, but not always, over 21. If a person had a guardian, the guardianship ended when they turned 21, and the guardian was supposed to turn over all assets they had been holding in trust. Note that when women with guardians married before they turned 21, the guardianship usually ended, as their husband was considered the best person to look after her interests.
Orphans, Guardians, and Binding Out
A child under 21 would be considered an orphan by the courts if either parent died, particularly if they inherited property through that parent. So, an orphan might have a living parent. If a child under 21 inherited property, a guardian would be appointed by the court to hold and protect the assets in trust until the child turned 21, or, in the case of women, married. The orphan did not always live with the guardian. The guardian was what we call a fiduciary guardian, entrusted to look after their child's inherited wealth. At 14, a child could choose their own guardian, with the consent of the court. Step-fathers were considered poor guardians, and often wasted the inheritances of their step-children, but step-fathers became guardians often. Orphans usually lived with relatives, but if he or she had no relatives nearby, or the family was poor, orphans would be "bound out" to an individual to learn a trade; the orphan was released from the contract at 21.