Book keeping and accountancy practically mean the same. However, they are different due to the following reasons.
Book-keeping
Bookkeeping is an art of recording financial transactions in original books and positing them into the ledger accounts. Under this, all business transactions may be recorded by the book-keeper. Lower level of staff can perform such job. It is just a part of accountancy.
Therefore, book-keeping is mainly concerned with recording of business transaction in the book of account.
Accountancy
Accountancy is wider term in which an account uses the books of account maintained by the book-keeper and prepares the trail balance and balance sheet.
It includes some vast principles and rules for which only the qualified staff can work as an account. Besides these, it involves many more activities like classifying and summarizing the events and transactions of business and interpreting their results.