違う: 【ちがう】(CHIGA-u)
to differ (from); to not be in the usual condition; to not match the correct (answer, etc.); to be different from promised
Example: 違う文化について学びたい。// Chigau bunka ni tsuite manabitai. // I want to learn about different cultures.
Example: この漢字は違うよ。// Kono kanji wa chigau yo. // This kanji is wrong.

異なる: 【ことなる】(KOTO-naru)
to differ; to vary; to disagree
Example: 異なる文化について学びたい。// Kotonaru bunka ni tsuite manabitai. // I want to learn about different cultures.
Example: この名前のつづりが異なる。// Kono namae no tsudzuri ga kotonaru. // The ways to spell this name differ.

(Kanji definitions from KanjiDic2.)

I do not claim to be a kanji expert. I can usually read a newspaper without difficulty, but if you asked me to read aloud I might struggle on a few words here and there. I, like many modern Japanese people, have also forgotten how to write a lot of kanji which I used to be tested on in school because I usually type them instead of write them. It’s sort of like how proper spelling in English is said to be a dying art form.

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