a sister: a female sibling, and by extension a woman who belongs to the same spiritual family
At its root this word names a female sibling, a daughter of the same parents. That plain family sense covers most of its appearances, from the sisters of Jesus mentioned by his neighbors to Martha and Mary, the two sisters of Lazarus.
The early church stretched the word past blood ties. Jesus said that whoever does the will of God is his brother and sister and mother, and the letters that followed pick up the same habit: a fellow Christian woman is called a sister, whether she is Phoebe serving the church, a widow to be treated with respect, or simply a believer in need. The bond of shared faith is spoken of as real kinship.
The two uses are not two different words but one idea carried a step further. English does the same thing, calling a woman in the same church a sister, so a reader rarely has to stop and decide which is meant. The context makes it plain: a named household points to blood family, while a greeting among believers points to the family of faith.
Nuances
Whether the elect sister in 2 John 13 is a personified sister church or the literal sister of an individual woman addressed in the letter.
- majorityThe elect lady of verse 1 is a congregation, so the elect sister is a sister church whose members send greetings.; BDAG, s.v. ἐκλεκτός and κυρία
- minorityThe elect lady is an actual woman, so the elect sister is her literal sibling.; H. von Soden, "ἀδελφός, ἀδελφή," TDNT 1:144-146