Since I don't want to be a wet noodle on the other Holi thread, I'll mention this here ... etymologically the two are distinct. Holiday (the English word) is derived from the same root as holy.
Holi (the Indian word) is derived from a legend involving fire.
From the Internet (and thus guaranteed, um lol):
"The celebration of Holi is very ancient in its origin. And by its very origin, it celebrates an ultimate triumph of the 'good' over the 'evil'. While, a feast of colors associated with the Holi, is the face of this celebration, the original reason of celebrating Holi, lies in its soul. And this gives us the 'why' of this ancient festival.
Literally "Holi" signifies "burning" in Indian language. But, how it came to be associated with 'burning', is a story. The reference is found only in ancient Indian mythology. And It is the legend of Hiranyakashipu, to whom the celebration of Holi is associated.
Way back in the pre-Christian era, there lived a demon king named Hiranyakashipu in ancient India. He wanted to avenge the death of his younger brother. The brother, also a demon, had been killed by Lord Vishnu, one of the supreme trio, monitoring the life and death in the universe, (according to the Hindu belief). To take on Vishnu, the tyrant king wanted to become the king of the heaven, earth and the underworld. He performed severe penance and prayer for many years to gain enough power. Finally he was granted a boon. Powered by the boon, Hiranyakshipu thought he had become invincible. Arrogant, he ordered all in his kingdom to worship him, instead of God. The demon king, however, had a very young son, named Prahalad. He was an ardent devotee of Vishnu. Despite his father's order, Prahalad continued to pray to Vishnu. So the demon king wanted to kill his son. He asked the favor of his sister Holika who, because of a boon, was immune to fire. They planned that Prahalad would be burned to death. A pyre was lit up and Holika sat on it, clutching Prahalad. Yet, at the end Prahalad emerged unscathed by the fire, And Holika, the demon, was burned to ashes. The earnest devotion and complete submission to Lord Vishnu savedyoung Prahlad. Thus was the triumph of Prahlad, the representative of good spirits. And the defeat of Holika, the representative of evil. Later, even the demon king Hiranyakashipu was killed by Lord Vishnu. But that is quite a different story. It is from Holika, that the Holi originated. This legend is relived even today on the Holi-eve when the pyre is re-lit in the form of bonfires. Even today, people celebrate this occasion. Huge bonfires are lit up every year on the eve of the full moon night of the Holi to burn the spirit of the evils. Hence the story associated with the soul of the celebration."
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