The words some, sum sound the same but have different meanings and spellings. Why do some, sum sound the same even though they are completely different words?
The answer is simple: some, sum are homophones of the English language.
Being an unspecified number or quantity: Some people came into the room. Would you like some sugar?
Being a portion or an unspecified number or quantity of a whole or group: He likes some modern sculpture but not all.
Being a considerable number or quantity: She has been directing films for some years now.
Unknown or unspecified by name: Some man called.
Mathematics An amount obtained as a result of adding numbers.
Mathematics An arithmetic problem: a child good at sums.
The whole amount, quantity, or number; an aggregate: the sum of the team's combined experience.
An amount of money: paid an enormous sum.
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").