The words ledger, leger sound the same but have different meanings and spellings. Why do ledger, leger sound the same even though they are completely different words?
The answer is simple: ledger, leger are homophones of the English language.
A book in which the monetary transactions of a business are posted in the form of debits and credits.
A book to which the record of accounts is transferred as final entry from original postings.
A slab of stone laid flat over a grave.
A horizontal timber in a scaffold, attached to the uprights and supporting the putlogs.
light; slender; slim; trivial
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").