In general, the overall objectives of the auditor, in conducting an audit of financial statements, are to (a) obtain reasonable assurance about whether the financial statements as a whole are free from material misstatement; and (b) report on the financial statements, and communicate as required in accordance with the auditor's findings.
An audit will typically be performed under certain auditing standards decided by an organization's financial statement users (e.g., its shareholders, regulators, lender, etc.) based on their goals and concerns; how an entity receives its capital or revenues is usually the deciding factor as to which auditing standards to follow. The different standards are similar in some ways and different in other ways, require more or less testing and reporting in certain areas, and they sometimes draw from or require adherence to each other.
Here are the major auditing standards in the United States and their typical users:
GAAS Audits (Generally Accepted Auditing Standards): private companies, non-profits
Yellow Book Audits (Government Auditing Standards): government entities, entities expending federal funds
PCAOB Audits (Public Company Accounting Oversight Board): publicly traded companies, broker-dealers
Single Audits (Uniform Guidance): entities expending federal funds