AAA is an organization that promotes worldwide excellence in accounting education, practice and research. AAA has around 8,000 members and publishes both "The Accounting Review" and "Accounting Horizons."
AICPA is an organization for CPAs. AICPA works closely with FASB to set standards and guidelines. AICPA has over 350,000 members and publishes the "Journal of Accountancy."
IFAC is a global accountancy organization. IFAC represents more than 2.5 million members and works with 158 member, associate and affiliate organizations in 123 countries (like AICPA and IIA in the United States).