In the case of fraud, as in the case of most kinds of legal terminology. There isn't one definition. Different definitions apply in different contexts.
Common Law Fraud Common law fraudulent misrepresentation in a lawsuit by the person harmed against the fraudster for money damages requires a knowingly false statement of a presently existing material fact made with an intent to mislead, that is justifiably relied upon by the defrauded person in a manner that causes damages to that person. Fraudulent concealment is similar but also involves a set of rules regarding when someone has a duty to make a statement to prevent someone from relying on its absence.
Intent without Damages. Many criminal and consumer protection statutes, for example, eliminate the elements of proof of damages and justifiable reliance on the fraudulent statement or omission, that is present in the common law torts of fraudulent misrepresentation and fraudulent concealment. But the defrauded person can't usually sue or can only sue for a statutory fine.
Misrepresentations To Someone Who Is Not Personally Harmed There are also fraud-like torts that govern cases where a representation is made to one person upon which that person relies causing harm to another person. Defamation and slander of title are two of the more common ones. Lanham Act misrepresentations about goods also fit in this category.
Other torts that are sometimes "fraud-like" including and intentional interference with a contract or prospective business advantage, and "false light" privacy invasion cases also fit in this category.
Liability For Knowable Or Immaterial As A Matter Of Law Statements Real estate disclosure statutes often specify that certain matters are material even if they would not have been considered material under common law precedents or would have been "patent defects" which there otherwise would have been no duty to disclose.
The common law fraud requirement that a fraudulent misrepresentation concern a presently existing material fact is relaxed somewhat in statutory securities fraud claims to include opinions and statements about the future that are misleading from which a reasonable person would infer a statement about presenting existing facts.
Lack Of Informed Consent And Heightened Duties The duty to disclose is higher between people in a confidential or fiduciary relationship (essentially "informed consent") than it is between competent strangers dealing at arms length. The can overlap with legal consequences for exercising "undue influence" over someone who is vulnerable (essentially putting words in their mouth since you control them psychologically and contrary to their wishes if not under the person's influence).
The definition of fraud in the context of an ex parte representation to a court is much broader and encompasses more kinds of statements (basically a duty to tell both sides of the story as to both law and fact), than common law fraud.
Procedural Low Thresholds For Fraud The definition of fraud for purposes of the requirement to describe with particularity the events giving rise to a claim in a complaint filed with a court is broader than the definition of common law fraud.
Actionable Representations Made Without Fraudulent Intent Some kinds of statements are actionable with certain remedies when made about securities even if they are true as a form of securities fraud, including all statements made about unregistered securities that are not exempt from registration.
A warranty and representation that a fact is true made in a contact is actionable in a lawsuit if it is not true, even if the warranty and representation was made believing it was true. A false representation concerning good for sale made without intent to defraud is deemed to be an express warranty under the Uniform Commercial Code.
Negligent misrepresentations (usually only in connection with a business or occupation) can give rise to liability in a lawsuit.
N.B. The term "lying" is usually reserved for intentional fraudulent misrepresentations and is also strongly disfavored by judges both in their own statements and in statements by parties and counsel.
Privileged Falsehoods Intentional false statements regarding immaterial facts are usually not actionable and usually don't give rise to legal liability.
Neither are intentional false statements made, for example, in the course of political campaign or in religious preaching.
Many false statements made to induce non-commercial sex or marriage are also not actionable and are not a basis for criminal liability.