Only one English translation of this work has been published, the one by Aileen Tone (and this is only of the first volume of the original two-volume work). You can find a pdf of it here. The Solesmes page states only that Justine Ward "went to great lengths in order to assure an English translation" of the work and that it was done "thanks to her," not that she made the translation herself.
The story of Ward's involvement with the translation is told in the second chapter of the book Justine Ward and Solesmes by Dom Pierre Combe (CUA Press, 1987) which can be found on Google Books.
Thanks everyone for replying to my question. I got a response from Fr. Geoffroy Kemlin from Solemes saying that they are indeed different, but I'm sure of the differences between the two books.
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