Huzzah may be categorized with such interjections as hoorah and hooray. According to the OED, "In English the form hurrah is literary and dignified; hooray is usual in popular acclamation."
In common usage, such as cheers at sporting events and competitions, distinction need not be made by the speaker and the words are distinguished by regional dialect and accent.
Hooray comes from the Mongolian Hurree, used by Mongol armies and spread throughout the world during the Mongol Empire of the 1200s. In Mongolian Hurree is a sacred praise much like amen or hallelujah.
The OED notes that in the 17th and 18th centuries it was identified as a sailor's cheer or salute, and thus was possibly related to words like heeze and hissa which are cognates of hoist. This behavior is depicted in the Disney movie Pirates of the Caribbean: Curse of the Black Pearl.
In the 18th and early 19th centuries, three 'huzzahs' were given by British infantry before a charge, as a way of building morale and intimidating the enemy. The book 'Redcoat' by Richard Holmes indicates that this was given as two short 'huzzahs' followed by a third sustained one as the charge was carried out.
"Huzzah" is also the exclamation used by the slapstick villain Punch as he outwits the Devil in the finale of the classic version of the Punch and Judy show, which dates back to the 18th and 19th centuries in England.
"Huzzah" is also the exclamation cheered by the South Carolina Militia upon the arrival of Colonel Benjamin Martin (Mel Gibson) carrying an American flag on his horse in the 2000 Revolutionary War film The Patriot.