I've been digging a little further and have come to the conclusion that although a robe à tournure and a robe à pouf are both bustle dresses or gowns, the difference between them, in so far as there is one, is the nature of the device worn under them. A tournure is a frame, like a crinoline but just at the back:

"elle est elle aussi [comme la crinoline] constituée d'un réseau de baleines métalliques horizontales, soutenues par des bandes verticales. Cependant, elle ne couvre plus que l'arrière"
http://fr.wikipedia.org/wiki/Tournure

"A bustle is a type of framework used to expand the fullness or support the drapery of the back of a woman's dress, occurring predominantly in the mid-to-late 19th century."
http://en.wikipedia.org/wiki/Bustle

Whereas a pouf is a pad or cushion, often apparently stiffened with whalebone (pouf baleiné):

"Qu’est ce qu’une crinoline ? A l’origine un jupon d’étoffe raidie de crin, la crinoline devient en 1859 une cage armaturée de cerceaux métalliques dont le diamètre peut atteindre 180 cm. Sa forme évolue de ronde à projetée (volume vers l’arrière) pour se transformer en tournure ou en pouf (coussin sur les reins) à partir de 1867."
http://www.lyceumfrance.org/Exposition-au-Musee-Galliera,270

Note the date and compare the reference to Worth's innovation I quoted in the discussion: it may well be that his contribution was to use a cushion rather than a frame.

I think this distinction, such as it is, has become rather obscured. The Trésor doesn't seem to recognise this meaning of pouf, but its definition of tournure really covers both:

"Rembourrage porté sous la robe, en bas du dos, afin de lui donner plus d'ampleur."
http://www.cnrtl.fr/definition/tournure

What is interesting is that it illustrates this with a passage from Balzac dated 1846:
"Caroline marche à la Elssler, en agitant sa tournure de la façon la plus andalouse"
If Balzac is referring here to a bustle, clearly Worth didn't invent it; he presumably therefore introduced a different, softer, perhaps smaller type of bustle. But I'm speculating here.

My first suggestion comes from here:
"Cabinet card photo of a young woman in a high-neckline, pouf style bustle dress accented with velvet stripes circa late 1870's to the 1880's."
https://www.etsy.com/ie/listing/217091435/cabinet-card-photo...

The second is from here (sorry about the caps):
"THE PATTERN INCLUDES THE CIRCA 1883 BUSTLE PAD DRESS WITH OVERSKIRT, BUSTLE PAD, BACK DRAPE AND PLEATING AT THE HEMLINE"
http://www.worthpoint.com/worthopedia/17-18-antique-french-f...

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Note added at 1 hr (2015-05-20 17:53:58 GMT)
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I must admit that Littré, who is bang on the right period, doesn't distinguish a pouf from a tournure:

"SUPPLÉMENT AU DICTIONNAIRE
3. POUF. Ajoutez :
3° Sorte de tournure que les femmes se mettent par derrière.
• Quand tu seras juponnée un peu plus haut par derrière, avec un pouf convenable...., OCTAVE FEUILLET Rev. des Deux-Mondes, 1er mars 1872, p. 7."
http://littre.fracademic.com/54221/pouf

However, Guy Robert gives me a little more ammunition with this definition he quotes from "Ac8", presumably the 8th edition of the DAF:

"POUF
Se disait d'une coiffure de femme [those enormous Marie-Antoinette-style contraptions] et aussi d'une sorte de coussin de tournure, qui se plaçait par derrière, sous la jupe, au-dessous de la taille"
https://books.google.es/books?id=PxYEW56qVGgC&pg=PA1810&lpg=...

Note "coussin DE tournure": I take this to indicate that tournure is the generic word for bustles of all kinds and pouf is specifically the pad or cushion type.