At Common Law:
Definition: “Wrongful detention amounting to repudiation of the owner's rights or any exercise of dominion inconsistent with such rights.”
Conversion is a tort. Tort claims are enforced by filing a private lawsuit for damages, i.e. a money judgment directing the defendant to pay for the property or the use of the property.
A lawsuit is only worth the trouble when you are likely to be able to collect the money. If the thief is a corporation, it makes sense to sue to collect a judgment in the amount of what you lost, rather than having the government levy a fine or jail a CEO. If the thief is a deadbeat, you rely on law enforcement authorities to punish the theft, as a crime.
Theft, larceny, embezzlement etc. are crimes enforced by a public lawsuit (i.e. the district attorney files criminal charges). If convicted, the defendant must pay a fine or do jail time. Crimes are wrongs against the people (the sovereign); torts are wrongs against a private person.
"Conversion" can also be distinguished from the writ of replevin. A writ of replevin is a court order to give the property back. A suit for "conversion", on the other hand, does not ask for the property, it asks for money.
“Conversion” occurs when the defendant was supposed to give the property back, but instead deliberately kept it, intending not to return it. For example, if you rent a car, but fail to return it, you have “converted” the car.
"Conversion” also occurs when you take something before it belongs to you: if you order something with a credit card, and they charge the card before shipping, they have “converted” your money.
Finally, “conversion” includes borrowing things that don’t belong to you, but in that case the damages are limited to rental value for the period of “borrowing”, not the market value of the entire item.
The mind of haze
W. Page Keeton et al., Prosser and Keeton on the Law of Torts, Ch. 3 § 15 (5th ed. 1984).
Restatement (Second) of Torts § 223 (1965) (listing seven ways by which conversion may be committed)