The words absence, absents sound the same but have different meanings and spellings. Why do absence, absents sound the same even though they are completely different words?
The answer is simple: absence, absents are homophones of the English language.
The state of being away.
The time during which one is away.
Lack; want: an absence of leadership.
The state of being absent-minded; inattentiveness: absence of mind.
Third-person singular simple present indicative form of absent.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition, from Wiktionary, Creative Commons Attribution/Share-Alike License 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").