Compilation and review engagements are similar to audit engagements in a few ways. In all three types of engagements, the CPA performs certain procedures in accordance with professional standards before issuing a report on a set of client financial statements. The major difference between those engagements is the level of assurance the CPA provides in the report.
An audit provides the highest level of assurance. In an audit engagement the CPA will carry out procedures to obtain an understanding of internal control, and perform substantive tests of transactions. They will also use analytical procedures on financial data and perform tests of details on account balances.
A Review Report expresses limited assurance that there are no material modifications that should be made to a set of financial statements in order for them to be in conformity with a particular basis of accounting. A Review Report provides less assurance than an Audit Report, but also requires less work by the CPA, which results in a lower fee. In a review engagement, the CPA will use analytical and other procedures on the financial data.
A Compilation Report does not express an opinion or provide any assurance about the fairness of a set of financial statements. In this type of engagement, the CPA merely submits client information in the form of financial statements, and is not required to perform any verification procedures.
Not For Profit Organizations are often required to have a CPA Audit or Review because of state requirement or at the request of funders.
The AICPA has a useful guide to understanding the difference levels of service the Certified Public Accountant performs.