prefix
not yet; un-; incomplete
Prefix that attaches to nouns and na-adjectives to express that something has not yet happened, is not yet complete, or is in an un- state. Common in formal and written language.
未完成の作品を展示する。
Exhibit an unfinished work.
その問題は未解決のままだ。
That problem remains unresolved.
非 means 'non-' or 'anti-' and often implies a stronger negation or opposition, whereas 未 focuses on something not having occurred or not being completed.
From the kanji 未, which originally depicted a tree with new branches, symbolizing 'not yet' or 'immature'. The prefix use derives from this meaning.