joy: the glad lift of the heart at something genuinely good
Joy is the standard New Testament word for gladness, and on the surface it is ordinary everyday Greek: people feel it at good news, at a reunion, at finding treasure, at a child being born. That plain emotional core never goes away. But the New Testament writers fill the same word with a fuller content. Again and again the joy they describe is not produced by good circumstances but given by God himself, carried by his Spirit, and tied to Jesus, so that it can survive and even grow in hardship. This is why the same word can mean a city's delight at hearing the gospel and also a settled gladness that an imprisoned apostle commands his readers to keep on having.
The senses below are not different words but one word seen from different angles. The first is the plain feeling of gladness. The second is that gladness as something God gives and the Spirit produces, the kind that holds firm under suffering because its source lies beyond what suffering can touch. The third is rarer: joy as the blessed state itself that a faithful servant is welcomed into, gladness pictured as a place to enter rather than a feeling to have. The fourth is a natural figure of speech, where a person who makes you glad is simply called your joy.
The word is closely tied in sound and root to the word for grace, and several writers, Paul especially, play on that link: joy is the heart's answer to God's grace. That connection is theological and felt, not a difference in dictionary meaning, so it colors the word without giving it a separate sense.