The words slough, sluff sound the same but have different meanings and spellings. Why do slough, sluff sound the same even though they are completely different words?
The answer is simple: slough, sluff are homophones of the English language.
A depression or hollow, usually filled with deep mud or mire.
A stagnant swamp, marsh, bog, or pond, especially as part of a bayou, inlet, or backwater.
A state of deep despair or moral degradation.
The dead outer skin shed by a reptile or amphibian.
The skin shed by a snake or other reptile.
Dead skin on a sore or ulcer.
an avalanche, mudslide, or a like slumping of material or debris
to shed, remove, get rid of, slide (off)
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").