Exalt is what you do to someone or something else, such as praising, honouring or raising it up. Exult is what you do yourself, when you rejoice, especially after a triumph. If you exalt the winning team, the fans exult.
The core difference
Exalt directs praise or status onto another person or thing; exult describes your own feeling of triumphant joy.
- exalt — to praise, honour or raise in rank: The critics exalted her debut novel.
- exult — to rejoice, especially in triumph: The crowd exulted as the final whistle blew.
How to tell them apart
A useful trick is the object. Exalt almost always needs something or someone to act on: you exalt a leader, a virtue, an achievement. Exult stands alone, or takes in or over: you exult in a victory, not exult a victory.
The mix-up tends to show up in formal or ceremonial writing, where both words appear in the same sentence about celebration, and a writer reaches for the more familiar-looking one without checking which way the action points.