Conversion is the unauthorized assumption and exercise of the right of ownership over property belonging to another to the exclusion of the owner's rights.  Where the property is money, a plaintiff is required to allege that it owned the money:

Thus, a claim of conversion will be governed by the technical rules of ownership.  For example, if the plaintiff wires his money into the defendant's account, and the defendant absconds with it, that's not conversion.  That's because, under banking law, once the money enters the defendant's account, it becomes the defendant's money.  Thus, the defendant can do what he wants with it without committing the tort of conversion.

Under the law of conversion, a lien on property is an interest in the property.  Thus, exercising control over property encumbered by a lien may constitute a conversion of the lien holder's property.  For example, if a lender has a security interest in collateral, moving the collateral may constitute a conversion of the collateral. 

Significantly, the intent that's required is an intent to exercise dominion over the property, not an intent to exercise dominion over property that the defendant knows to belong to someone else.  In other words, it doesn't help the defendant that he thought he owned the property.  He has still committed the tort of conversion.