Picture a school building that belongs to the streets around it. The people who study there live nearby, the money that keeps it open often comes from nearby, and its doors open for local adults too, not only for its own students. That is the whole of the word community here. What changes between the two meanings is only the age of the students and the level of the teaching: in the US it is a two-year college for adults after school, and in the UK it is a secondary school for teenagers that also serves the grown-ups next door.
From the word’s history
Wiktionary notes that the name comes from the fact that these colleges mainly attract and accept students from the local community, and are often supported by that community through property taxes.
Wiktionary 的詞源說明指出，這個名稱來自這類學校主要招收當地社區的學生，而且常由當地社區透過房屋稅支持。所以 community 指的是「誰來讀、誰出錢」，而不是課程的內容。
Wiktionary, entry 'community college' (packet evidence, source_ref kaikki:3f6f69a190036ae4:1470910032:4226)
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