Hi and High are easily confused words. The spell-check application of most word processing software programs would not catch a slip-up of these two words. Spell-check is looking for words that aren’t in its dictionary, and words that resemble words in its dictionary but are possibly spelled wrong. Spell-check isn’t perfect. It doesn’t know and can’t guess what word you wanted or what word you meant, it can only judge the words on the page. If you used words that are all spelled correctly, it gives you a pass anyway.
Hi is an interjection, short for “hello.”
High is an adjective, indicating a position in the air.
It can also be an adverb in the sense of rank, degree, or relative position to something else.
It can also indicate a feeling of elation, or carefree “floating” feeling in their head though the speaker hasn’t actually physically moved, their feet haven’t left the ground. (This is the feeling drug users describe after taking marijuana, hallucinogens, cocaine, and other currently illegal substances.) Athletes who pushed their physical limits often describe a “runners high” after exerting themselves.
High is found in a lot of idioms, far more than I can get into one blogpost.
The following sentence uses both words correctly:
Heidi was a cheerful, outgoing personality who said hi! to everyone on the trail in the high Alps.