“Exult” means to rejoice greatly, to be jubilant or triumphant. As we see in Psalm 5:11 – “But let all who take refuge in you rejoice; let them ever sing for joy, and spread your protection over them, that those who love your name may exult in you.”
“Exalt” means to raise in rank, to glorify, or to increase the effect or intensity of. So it is appropriate to glorify the name of the Lord as in “Oh, magnify the Lord with me, and let us exalt his name together” (Psalm 34:3)! However, it is never fitting or proper to promote ourselves as Psalm 66:7 tells us: “…let not the rebellious exalt themselves.” It is suitable only for the Lord to be exalted and to exalt the humble in due time. “Wait for the LORD and keep his way, and he will exalt you to inherit the land…” (Psalm 37:34 ESV).
“Exult” or “exalt?” These are definitely two words to keep straight and to put into practice.