What's the difference between a "normal" audit and a fraud audit?

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Normal Audit, is an assurence expressed by Auditors that financial statements are free form material miss statements and are in accordance with internationally accepted accounting framework

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Fraud Audit, is based on actually detected or suspected fraud in a company.

Most of the people think that purpose of normal audit is to detect fraud in any organization, this general perception is completely wrong.

According to ISA240, "Its not responsibility of auditors to prevent or detect fraud, its responsibility of management and those charged with governance"

so these both audits differ in accordance with ISA240.

The goal of a normal audit – how most people think of it – is for an independent accounting firm to express an opinion as to whether a company's financial statements are fairly presented. Essentially, the company prepares the financial statements and asks the audit firm the question, "is this correct?"

A fraud audit is a separate engagement from a financial statement audit. In a fraud audit, there typically is an allegation of fraud or a fraud has already been discovered; the accountant is called in to gather evidence or to act as an expert witness in connection with legal proceedings relating to the fraud. He or she is not asked to give an opinion on the financial statements as a whole.

From my point of view you both have right.

But fraud audit can be done also from different reasons, not just if the company have fraud allegation or if fraud is detected. Those situations you have described are reactive, but in case to prevent the fraudulent behavior we - or the company - can be also proactive. 

In any well-managed business entity there are some proceses and policies, also ethical code, some company's presentable behavior. Something what creating the honesty and good name on the market. And to protect that important value we can check the compliance of all what is described above. To fight against the fraud. The target is to preventive eliminated allmost all posibilities how to fraud, to check and verify the all weak points of company's proceses and to eliminate the posibility of destroying of the good name on the market.

The fraud audit is very powerfull preventive tool.  

Normal audit does not specifically focus on fraud activity but it included some testings, but fraud audit for fraud identification with anti fruad specialist 

The one that you call 'Normal' Audit consist in possibly scanning any activity in the business that might bring you losses or cause discrepancy  (cash, products, inappropriate behavior from your employees) or might put in danger you company like security risks. This Audit might generally last from5 to8 hours in a retail business. The Audit should possibly have a score in order to understand the level of your business and try to raise it standards. For this is is advised to insert suggestion and recommendation to increase the level of you business. In case of bad Audit it is recommended to come back after max days in the stores and control if your suggestions were put in place. 

The 'fraud' audit should be short and need a preparation because it is already given to you for your data or analysts names, facts and losses. It is a targeting audit. The most important part in this audit is being able to close the circle of the investigation by obtaining back the refund of your losses and completely terminate the contract with the person that performed the fraud. Most of the companies has a zero tolerance policy for internal theft.

The goals are different: one has the goal of determining the material correctness of the financial statements, and the other has the goal of uncovering fraudulent activity.

The goal of a normal audit – how most people think of it – is for an independent accounting firm to express an opinion as to whether a company's financial statements are fairly presented. Essentially, the company prepares the financial statements and asks the audit firm the question, "is this correct?"