The word rejoice
is very common in the Bible, far more so than the word exult.
There is no fundamental difference in the meaning of the two words. By piling one on top of the other, the servants singing this song express the abundance of joy that befits those who benefit from God’s truth and justice. In so doing they flesh out what’s implicit in the summons Hallelujah
; God is praised through his people being joyful on account of his salvation.
7 Let us rejoice and exult and give him the glory, for the marriage of the Lamb has come, and his Bride has made herself ready;