The words leaf, lief sound the same but have different meanings and spellings. Why do leaf, lief sound the same even though they are completely different words?
The answer is simple: leaf, lief are homophones of the English language.
A leaflike organ or structure.
Leaves considered as a group; foliage.
A usually green, flattened, lateral structure attached to a stem and functioning as a principal organ of photosynthesis and transpiration in most plants.
The state or time of having or showing leaves: trees in full leaf.
Archaic Ready or willing.
Readily; willingly: I would as lief go now as later.
Archaic Beloved; dear.
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").