This has been, your Japanese lesson for the day.
XD

Yes, やっと and やった are different words… but it is a little strange to see someone happily/excitedly shouting やっと in an exclamation of accomplishment.

やっと (adv) (1) at last; at length; (2) barely; narrowly; just; by the skin of one’s teeth

While in English we could shout “finally!” or “at last!” with exuberance, our meaning when we use the words in that sense is “hooray!” Using a literal translation of the English words doesn’t match the spirit of the speaker’s intent. If you try to imagine someone shouting the other variations of やっと in English, it begins to sound weird: “At length! Just barely!”

These other translations shed some light on the nuance of what やっと actually means to a native speaker. It also helps explain why やった would have been a more natural choice, as やった is used in this exact context (an exclamation of “we did it!”) in Japanese all the time.

Yatta and Yatto are two different words.