We often hear these two expressions used interchangeably, probably because of their paronymy, and we therefore tend to confuse them. In the same way, the terms "attention" and "intention" are sometimes confused when an expression like "à l'intention" is used for "à l'attention".
Definition of quick
The expression "in a jiffy" means that something is done quicklyor at least as fast as you can turn your hand. The same meaning is generally given to tour de main. This "On" includes, of course, the most important dictionaries... Note, however, that tournemain is rarely seen except in the expression "en un tournemain", while "tour de main" is used with variations: un bon tour de main.
Émile Littré explains in his Dictionary of the French language that in his day, at the end of the 19th century, "we'd rather say en un tour de main", then adds "when we want to express something that's done quickly, we should say: en un tournemain, and not: en un tour de main." Littré goes on to specify that tour de main refers to "an act of skill performed with the hand".
In its 8th edition, the Académie française adds that the locution has aged and condemns it, so to speak. Sleight of hand or sleight of hand?
Definition of tour de main
In his Dictionary of medicine, surgery, pharmacy, veterinary medicine and related sciences... (1884), Littré gives the following definition:
"Fam., In a jiffy, In as little time as it takes to turn your hand.
We took the case off in a jiffy. I would have done it in a jiffy. Some say and write, En un tournemain."
But it also indicates " Turn of hand, turn of subtlety, turn of skill. This escamoteur, this goblet player does some amazing tricks."
Whether we refer to etymology or usage, we can see that the expressions tend to be used for each other. And it's also understandable that vocabulary has a certain propensity to simplify, if only because we're unaware of their paronymous status.
I'll mess you up in a jiffy!
Petit Larousse and Grand Robert keep their dictionaries up to date with the latest French expressions. They regularly introduce new words, as if they were afraid that literature wouldn't appropriate them. Or that the little people would appropriate them before they did? Like them, the Académie's dictionary seems to endorse certain usages, but at a more modest pace. Whether it's the Trésor de la langue française or the Encyclopédie, our lexicographers compare research and points of view from all eras, and, above all, bear witness to the use of words by those who could write, whatever their level of mastery of the language of their time... Quarrels between linguists and grammarians will only serve to retrace the history of words and enrich encyclopedic knowledge, a treasure trove. The rule is an attempt to simplify an overly complex code, to establish a glossary or lexicon for the French-speaking community, but it's not a compulsion to take for granted what the first dictionary claims! When one expression is replaced by another, the French language is impoverished. When we neglect to do our job as lexicographers, we contradict ourselves...
Quick turnaround & execution, sleight of hand & skill
In any case, the two expressions continue to coexist, but any lover of the French language will recognize that it's easy to understand that speed of execution and address are confused, if only because it takes a good hand to execute a gesture quickly. And let's not forget that in the 3rd edition of its dictionary (1740), the Académie specified that tricks of the trade are "tricks of subtlety & dexterity that are done with the hands" and she adds this definition of tour de main in the 1937 edition Fig. and fam, Have a knack for it, To have the way, the skillpractice.
Contradicting oneself is still saying something, but it's not convincing. In short, it's usage that will prove the Académie and the dictionaries right, or not! In the meantime, feel free to make the distinction between the two expressions, and use either of them!