The words lichen, liken sound the same but have different meanings and spellings. Why do lichen, liken sound the same even though they are completely different words?
The answer is simple: lichen, liken are homophones of the English language.
A fungus, usually of the class Ascomycetes, that grows symbiotically with algae, resulting in a composite organism that characteristically forms a crustlike or branching growth on rocks or tree trunks.
Pathology Any of various skin diseases characterized by patchy eruptions of small, firm papules.
To cover with lichens.
To see, mention, or show as similar; compare.
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.