The words core, corps, kor sound the same but have different meanings and spellings. Why do core, corps, kor sound the same even though they are completely different words?
The answer is simple: core, corps, kor are homophones of the English language.
The central or innermost part: the hard elastic core of a baseball; a rod with a hollow core.
The hard or fibrous central part of certain fruits, such as the apple or pear, containing the seeds.
The basic or most important part; the essence: a small core of dedicated supporters; the core of the problem. See Synonyms at substance.
A set of subjects or courses that make up a required portion of a curriculum.
A separate branch or department of the armed forces having a specialized function.
A tactical unit of ground combat forces between a division and an army commanded by a lieutenant general and composed of two or more divisions and auxiliary service troops.
A body of persons acting together or associated under common direction: the press corps. See Synonyms at band2.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.