Same Word, Different Kanji

Sometimes in Japanese, a single word is spelled with different kanji. This can happen for multiple reasons.

Primarily, those different kanji may have slightly different meanings, and in writing they can specify which is the meaning of the word. This happens when a word can be used in multiple different ways.

For example, the word hayai はやい means either "fast" or "early," but if you're fast you're probably getting there early, and if you're early it was probably because you were fast, so they mean almost the same thing most of the time.

In writing, different kanji specify the meaning of the word. If it's hayai 早い, it means "early," if it's hayai 速い, it means "fast." To be honest, I'm not sure if they're the same word or different words that are homophones, but that's how it works.

Another example: the word atsui あつい, "hot." Because atsui 熱い is the antonym of tsumetai 冷たい, "cold," but atsui 暑い is the antonym of samui 寒い, "cold."

A more complex example: noboru 上る is a generic "to go up," noboru 登る means "to go up [by climbing]," and noboru 昇る means "to go up [in the sky]."

In Japanese, such words would be called doukun'iji 同訓異字, literally "same-reading different-character." Here's a list of them: https://joyokanji.info/iji.html

There are also cases where a word technically should be written with a given kanji, but that kanji is not a jouyou kanji, that is, it's not one of the most commonly used kanji, so instead one of the common kanji of similar meaning is used instead.

For example: kaiten 廻転, "rotation," is normally written as kaiten 回転, because 廻 is not jouyou, but 回 is.

Finally, in rare cases, a word may become a gikun 義訓, an "artificial reading," for a kanji or kanji compound. This happens when the author simply wanted to associated that word with the kanji and vice-versa. For example, writing the word ato 後, "later," with the kanji for "future," mirai 未来.