The words emergence, immergence sound the same but have different meanings and spellings. Why do emergence, immergence sound the same even though they are completely different words?
The answer is simple: emergence, immergence are homophones of the English language.
The act or process of emerging.
A superficial outgrowth of plant tissue, such as the prickle of a rose.
The act of immerging or plunging or sinking into or under anything; immersion: as, immergence in water.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition, from The Century Dictionary and Cyclopedia 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").