甲 vs 理 why one or the other

is there a time when you would use one vs the other, like reason meaning cause and reason meaning line of thinking or something? i know in english we use right in different ways and was wondering if this was something similar, like we use right in terms of moral/ethical/fair, we use it in terms of objective correctness or a response to an answer, and a direction. which i think corresponds to 正, 当, 右 respectively at least thats how it seems to have contextualized so far

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I think you meant to enter 由 and not 甲.

Neither of these are terribly common as stand-alone words (both around 10K frequency, so not terribly rare either), and they both appear frequently in compounds that don’t necessarily have a clear connection to reason in either sense. For example, 料理(りょうり) means cooking. But 料 most commonly means “fee” as in charge? They can also appear together in the word 理由 (りゆう)which means reason as in pretext or motive.

Attributing a meaning directly to kanji can definitely be helpful for a learner, but very often they don’t really have an actual meaning “as kanji,” and it can be useful to keep in mind that this is often more of a learner’s aid than how Japanese necessarily works. In some cases, like 火, there’s definitely a consistent meaning. In others, like 殆, well: ほとんど (most or hardly) can be written 殆ど but it also appears in 危殆 (きたい), danger. Which of those meanings you riff off of to find your “keyword” for 殆 is ultimately arbitrary.

That’s all to put in context what WaniKani is doing for you. You asked when you “would use one or the other,” but it’s a misguided question if you’re asking that based off the kanji they taught you. You can ask this question about words, but you can also ask it about which kanji are used in which words, and they’re very different questions. Kanji themselves are not words (although some words are written with single kanji), and there isn’t always going to be a clear connection between a keyword you might have learned for a kanji and the vocabulary that uses it. (Or if there is, it may be so buried in etymological history that it’s still not going to help you, unless you just have an interest in putting extra work into etymology.)

Overall, you’re basically right, but that comes with very big caveats that it’s important to keep in mind moving foward. If you ever want to double-check your understanding of a kanji’s general meaning, I recommend entering it in JPDB and clicking the “More information” tab to get a thorough list of words using that kanji. Like here: 理 – Kanji details – jpdb

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Did you perhaps mean 由?

You’d use one or the other because that’s how words are spelt. Like, you wouldn’t spell 自由 with 理 because the word is 自由. And you wouldn’t spell 理論 with 由 because the word is 理論.

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I often compare kanji as a whole and their place in Japanese to English root words. The roots mono and uni both mean one, but they come from different languages of origin and are used in different words. United is not monoted and a monopoly is not a unopoly. While all kanji are derived from Chinese characters originally, the words they’re used in are sometimes Japanese in origin, predating the import of Hanzi and sometimes loanwords from Chinese so some kanji compounds make perfect sense going from the individual meanings of kanji to the collective meaning and some don’t.

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