chairō

This is the ordinary New Testament word for being glad. It covers the whole range of joy, from a quiet inner contentment to open, demonstrative celebration, and it is used of people, of God, and even of love itself taking delight in the truth.

Much of its range is simply a matter of what the gladness is about and how strongly it is felt. Sometimes the word stands alone for plain happiness; sometimes it points to the thing that causes the joy, naming what someone is glad about or glad over. The shift is in the occasion, not in the core feeling.

A distinctive New Testament use turns this gladness into something a believer is told to do, and to do even when life gives no natural reason for it. Here joy becomes a settled response that does not depend on circumstances, so that it can hold steady, and even grow, in loss, hardship, and persecution.

Besides meaning to rejoice, the same word served as the everyday word of greeting, the way one person hailed another in person or opened a letter. Literally it says "rejoice," but in practice it had worn down to a polite "hello" or "good day," much as our own greetings no longer carry their original sense.

In face-to-face speech it is the word the soldiers throw at Jesus when they mock him as a king, the word of Judas at the betrayal, and the word the angel speaks to Mary. In letters it is the standard opening, where it functions as our "greetings" rather than a wish for joy.

Because the word literally means rejoice, the line between a real wish for joy and a mere greeting is sometimes thin, and a reader has to weigh the setting. To welcome someone in this way could even count as endorsing them, which is why one letter warns against extending the greeting to a false teacher.