@vikorr,
There are vast differences in the Accounting world. To be an irregularity, it must be proven by true evidence. Until proven, it is an anomaly. Having been an Accountant and Auditor for many years, well, as you see, there is a major difference.
1.
An accounting irregularity is an entry or statement that does not conform to the normal laws, practises and rules of the accounting profession, having the deliberate intent to deceive or defraud. Accounting irregularities can consist of intentionally misstating amounts and other information in financial statements, or omitting information required to be disclosed. Accounting irregularities are commonly distinguished from unintentional mistakes or errors.
Accounting irregularities are often committed as a means to an end, for example assets misappropriations may be concealed by using irregular accounting entries and profit overstatements may inflate the year end bonuses to perpetrators.
2.After sample is selected we examine it , perform audit procedures on it. Then we get misstatements / deviations.
Now if misstatement / deviation is such that it’s not going to repeat again and again then , for example it happened because employee got heart attack then such things are called anomaly.
Now anomalies are ignored while doing projections about misstatements / deviations in population, as they are of non recurring nature. Or, they show a change in the character and become the new norm.