Shortly it can be said that "Auditing is the process of verifying accounts".
Both are the branch of commerce and can be studied and practiced at a professional level individually.
Audit is the review and verification of books of accounts so maintained by the organisation keeping in mind the Standards of Auditing (SA). In India the Standards of Auditing are formulated and amended by Auditing Assurance Standard Boards (AASB)
Accounting on the other hand is the process of recording data and information through proper vouchers and document in the books of accounts to ascertain the current financial position of the organization and for other stake holders as well. Principles of Accounting Standards are followed which are formulated and implemented by ICAI