The words deem, deme sound the same but have different meanings and spellings. Why do deem, deme sound the same even though they are completely different words?
The answer is simple: deem, deme are homophones of the English language.
To have as an opinion; judge: deemed it was time for a change.
To regard as; consider: deemed the results unsatisfactory. See Usage Note at as1.
To have an opinion; think. See Synonyms at consider.
One of the townships of ancient Attica.
Ecology A local, usually stable population of interbreeding organisms of the same kind or species.
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.
If they are spelled the same then they are also homographs (and homonyms); if they are spelled differently then they are also heterographs (literally "different writing").