Wow, someone who searches and reads, rather than simply posts! Ok, you have my attention. Chien only posts on the Debt Collection forum so, in Tom Wolfe's phrase, I'll be the flak catcher for this one. But you can trust me - you'd get the same answer from Chien.
And to get a complete answer, I hope you'll bear with me for a little background and explanation, because I think you have the rights, but I agree that the terminology doesn't seem to exist. Chien and I are from the same state - California. It has probably the most extensive body of statutes relating to judgment enforcement, and all the terminology doesn't exist there either. Finally, while I believe that the rights exist in Florida, I'm not completely sure about the steps to effectuate them.
An assignment order is a creature of statute. It is a right to payments due or to become due to the judgment debtor and it is obtained by a court order requiring the debtor to assign those rights to the judgment creditor. The relevant portion of the statute reads:
708.510. (a) Except as otherwise provided by law, upon application
of the judgment creditor on noticed motion, the court may order the
judgment debtor to assign to the judgment creditor or to a receiver
appointed pursuant to Article 7 (commencing with Section 708.610) all
or part of a right to payment due or to become due, whether or not
the right is conditioned on future developments, including but not
limited to the following types of payments:
(1) Wages due from the federal government that are not subject to
withholding under an earnings withholding order.
(2) Rents.
(3) Commissions.
(4) Royalties.
(5) Payments due from a patent or copyright.
(6) Insurance policy loan value.
So you could reach all rent owed to a landlord-debtor, or royalties owed to a musician or writer-debtor or other types of revenue that is more erratic and variable than would be reached by a wage garnishment. I may have referred to money due from the debtor of a debtor. That is not the girlfriend-car situation, unless she has a contractual obligation to pay for him.
A turnover order is not even specifically referenced in California. It must be "read into" the statutes. Once a writ of execution issues, the judgment creditor may apply to the Court for an order directing the debtor to transfer to the levying officer (1) tangible personal property and (2) documentary evidence of title to property (like a certificate of vehicle ownership) or a debt (like a promissory note). And this can be done pending any claim of exemption that might be filed.
Now in both instances - assignment order or turnover order - we're talking about non-exempt personal property that you would otherwise have the right to seize pursuant to judgment but that can be difficult to find and/or reach. That's why I say that the right exists in most every state. It's the procedure that you need to work out.
In California, an assignment order requires a noticed motion, and I suspect that it would be the same elsewhere but that it could be done, if the creditor can show the court that there are non-exempt assets in or coming into the custody of a specific third party. In that respect, the result differs very little from a bank levy.
A request for a turnover order can be made orally and ex parte, say at the end of a judgment debtor exam. To be prudent, you'd have a form Order with blanks for the name of the debtor and the property to be transferred. As long as you've already obtained a writ of execution and asset exams are normally conducted in a courtroom, you already have a judge who can sign and a bailiff who can take.
After looking at your Civil Procedure & Practice statutes, sect. 55.205 and 55.208, pertaining to judgment liens and writs of execution, I think adequate rights are conferred to be entitled to the property I've discussed. FRCP 1.570 provides that enforcement of a money judgment "shall be by execution, writ of garnishment or other appropriate process or proceeding", which I think could encompass either assignment or turnover. And FRCP 1.550 provides that execution "shall issue on the judgment on the oral request of the party entitled to it". So I think that the building blocks are there, and it's a matter of identifying the property and persuading the Court of the need.