According to Jaspert, Berthold introduced Standard, also called Akzidenz-Grotesk, in 1896.

It rather was the other way round. Berthold introduced the first weight of Akzidenz Grotesk in 1896. It was Akzidenz Grotesk schmalfett (bold condensed). In English speaking countries Akzidenz Grotesk was sold as Standard.

Especially in the metal type era, ‘produced’ does not mean ‘introduced’, let alone ‘designed’. So when you find a Linotype catalogue which lists Akzidenz Grotesk as ‘produced by’ Linotype, it does not imply that Linotype designed that typeface. The same applies to foundry type in a similar way in many cases.

In the late 1950s Berthold licensed Akzidenz Grotesk to Linotype. Günther Gerhard Lange told me that the idea behind it was that the availability of Akzidenz Grotesk on Linotype’s line caster would enhance sales of Berthold’s foundry type. In those days, the Swiss Typography movement promoted the idea of specifying a single type family for house style projects (corporate design). In order to be able to design and produce corporate brochures and magazines with the typeface(s) as specified in a corporate design manual, the availability of such typefaces on line casters (such as Linotype and Intertype) or typesetting machines such as Monotype thus became crucial.

From my experience in doing some research on the origin of German sans serifs, I think that the listings at the Klingspor Museum website are rather accurate.
http://www.klingspor-museum.de/KlingsporKuenstler/Schriftgiessereien/Haa...
But the trouble with listings such as Jaspert, the Klingspor site and Wikipedia, is that they do not mention a source per entry … Unfortunately the entry of Akzidenz Grotesk in the PDF on the Haas foundry at the Klingspor site does not tell as from which year Haas has been producing Akzidenz Grotesk. Also the PDF does not include images which show how the typefaces that were produced by Haas such as Akzidenz Grotesk and Normal-Grotesque may have looked like. It would probably take to go through all of the sources mentioned at the last page to find out where Hans Reichardt (the author of this PDF) obtained this information from …

Fortunately, Indra Kupferschmid did so and found this specimen of Normal-Grotesk - Grotesque by the Haas’sche Schriftgiesserei here:
https://www.flickr.com/photos/kupfers/6198185700/
This specimen tells us that Normal Grotesk and Akzidenz Grotesk are different designs. The notes by Indra also tell us that we cannot rely blindly on names or their spelling.

The inaccuracies, incompleteness and missing references of Jaspert, Berry & Johnson’s Encyclopaedia of Typefaces and the Klingspor PDFs, combined with other people compiling informations from ‘mixed sources’ leads to curiosities such as this one here in the listing of typefaces as produced by Haas:
http://en.wikipedia.org/wiki/Haas_Type_Foundry
Profil, 1947, Eugen and Max Lenz, Bitstream
Of course, Bitstream (founded in 1981) has nothing to do with the ‘origin’ of Profil (issued by Haas in 1947) …

When talking about the history of Akzidenz Grotesk and Neue Haas Grotesk / Helvetica, one has to keep in mind that Französische Grotesk was one of the models that was used for the design of Neue Haas Grotesk / Helvetica.
https://www.flickr.com/photos/kupfers/5933679233/
On its turn, Französische Grotesk origins in Breite Grotesque by Schelter & Giesecke. Of which I think that it also served as a model for Berthold’s Akzidenz Grotesk. But the history of sans serif in Germany does not start with Schelter’s Breite Grotesque, of course … ;–)