ok, here is what I have found out.
Ok Lawrence, here are my results:
A) Miele Care Collection tabs (with water-soluable wrapper) are indeed made by Dalli. Dalli-Werke produces all kinds of detergents, a few of them are sold under their own Dalli brand, but most are relabled with fancy names to be sold as no-name or generic house brands of those retail chains and food discounters (Aldi, Penny, Netto, Rewe, the Rossmann chemists chain stores and all these).
B) Some of Mieles large-volume packs (60 and more pcs. per package) are made by Claro Austria. They always have this slanted box, not the square one.
C) While Miele carried a dishwasher salt of its own name, they returned to the Somat brand (Somat for Miele they call it) (a Henkel brand).
What it boils down to: I was not able to find out the exact product codes (no search tool would be able to find the numbers, USA, Canadian, European, German, just none).
But looking at ingredients lists and stuff like that I am more than positive that Miele Care Collection tabs are widely identical to the cheap Aldi "Alio Compact" (or Akuta komplett, as it is called in Northern Aldi regions).
The package is 2,99 Euros for 40 tablets.
I can send you one and you check it out.
Aldi USA should carry them, too.
Here are some links:
a.) Care Collection = Dalli
http://www.wer-zu-wem.de/handelsmarken/handelsmarken_haushalt.html (who belongs to whom)
http://www.aldi-sued.de/de/html/product_range/2744_18503.htm (Aldi Süd product page "Alio" tabs)
http://www.miele.de/at/haushalt/produkte/Reinigen_Pflegen_Geschirrspueler.htm (Miele page Care Collection).
b.) Slanted package = Claro Austria
http://www.monstermarketplace.com/kitchen-and-bathroom-hardware/miele-dishwasher-tabs-06848090 (Miele tabs)
http://www.claro.at/DE/Produkte/Geschirrspuelen/7in1-Multi-Tabs.htm
c,.) Multifunctional dishwasher tabs being tested by "Stiftung Warentest" (German counterpart of Consumer Report) text of test results and ranking table.
http://www.test.de/themen/haus-garten/test/Geschirrspueltabs-Somat-knapp-vorn-1847365-1848034/
http://www.test.de/themen/haus-garten/test/Geschirrspueltabs-Somat-knapp-vorn-1847365-1849960/
But to be on the safe side, I mailed your data to a friend who is working for some big chemical company here, he should perhaps find out more details (a well-known American corporation btw...)
But it might take us some while until he answers.
One funny thing that I came across when browsing all these sites:
"Tandil" (Aldi's laundry detergent) has a package design that tries to remind you of Henkel products while Aldi USA bottles almost look like Tide bottles). Generic brands living on the fame of others / market leaders....
So just shoot me a mail if you want Aldi tabs (in case you cannot get them).
Cheers, Joe