The words staff, staph sound the same but have different meanings and spellings. Why do staff, staph sound the same even though they are completely different words?
The answer is simple: staff, staph are homophones of the English language.
A stick or cane carried as an aid in walking or climbing.
A stout stick used as a weapon; a cudgel.
A pole on which a flag is displayed; a flagstaff.
A rod or baton carried as a symbol of authority.
Informal Staphylococcus.
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").