FYI, I'm not an attorney, this isn't legal advice, and you should seek an attorney in your jurisdiction if you have a real legal concern or potential case.
Detinue
Detinue seeks recovery of a piece of property that has been wrongfully held or retained (distinguished from replevin which seeks recovery of property that has been wrongfully taken). Under detinue, the defendant received the property legally and the plaintiff never had to have the property in the first place (so, say you have something that I am supposed to receive, but I've never had it and you won't give it to me).
Conversion
Conversion occurs when one purposely interferes with another's personal property. The plaintiff must show that he owns or has the right to have the item at the time it's interfered with, that the defendant's interference with it was intentional, that the interference deprived the plaintiff of possession or use of the item, and that the interference caused damages to the plaintiff.
Say I swipe a document off of your desk and walk out with it. Within 30 seconds, it would be unlikely you could claim conversion. Why? Because there had not yet been any damages to you. Now, if I had that document for three hours and you were supposed to file it in court for a deadline or something, and you could show I intentionally took it (aka did not mistakenly believe it was mine), you may then have a claim.
Also, conversion can happen if you receive an item from somebody who was not authorized to give it away from you.
Trespass to Chattels
This is an intentional and wrongful interference with another's possession of property. The difference between this and conversion is about the degree of interference. Trespass to chattels can be found where one merely challenges another's right of possession. However, if the offending party exercises "dominion and control" over the item, it's likely conversion.
To return to the document example, if I had it for those 30 seconds, you may not be able to claim conversion, as I stated, but you may be able to claim trespass to chattels in that situation.
Another example, for clarity's sake: someone steals your car and you recover it within 20 minutes. Probably trespass to chattels. Someone steals your car and sells it to another person. Probably conversion.
Single Cause of Action?
Detinue is almost in complete disuse, so you in fact may not need to worry about it. Most jurisdictions have statutes for the recovery of personal property which have largely superseded detinue. Detinue is an action to recover personal property belonging to the plaintiff. Trover is an action for the recovery of damages for the wrongful conversion of personal property. Mixed in with all this is replevin, which is an action where a party seeks the return of an item that was taken wrongfully pending the final determination by the court of its true owner (maintaining the status quo until it's figured out who should be entitled to keep it).
