Hi, Mr. Rodney. The website below may shed some light on what the term 'orphan' meant in 1777 although these records are from 1883. As you can see, even by that date, when there were orphanages available, not everyone sent there was an 'orphan' as we may understand the term. In New York City, for example, there was an institution in operation in the 1800's that took in 'half-orphans' and destitute children.

The children you found were fortunate in that they were with a family that provided for them. The year being 1777, I imagine more 'orphaned' children ended up in the homes of other families than in later years when orphanages became more widespread and recordkeeping made it harder to just take a child in off the street.

Spivey