'Früher' means 'formerly known as'.
They bought a number of companies and used the brand names if they saw that as an advantage. But DWF was an attempt to disguise the name after 1918. Deutsche Waffen Fabriken. It was shortlived. DWM changed into BKIW and DWF was dropped again.
Another example is Berka Werke that made cutlery.
DWM was quite big in ball bearings and that was an area where Hugo Borchardt was quite active in.
An interesting side note is that DWM Berlin rented out part of the complex to General Motors after WW1.
Mauser was pushed out of the car business because it conflicted with another car company the banks and board members had an interest in: Daimler-Benz.
One of the funnier DWM products after WW2 was the Ampficar.
Entertaining link, lying about their company history
https://www.iwk.de/en/company/history/
Illustrated: A tin box with a (still wrapped) DWM bicycle chain, a little spoon made by 'BERKAWERKE' (with DWM's 'bombe' logo) and a presentation card stating that it is an honorary gift from BKIW / DWM.
So, why all these name changes: It's simple, really. If your company is called German Weapons and Ammunition factory, and the Allies want to wipe out German's arms and ammo production, you're screwed.
The only thing DWM could do was try to mask and alter it's name and take up production of the largest quantity of household crap they could come up with. All this to avoid seizing of factories, equipment, tools and other assets. DWM went as far as to use their large ammunition production machines to produce cutlery, buttons, buckets, etc... Apart from that, they moved some of their heavy tooling across the border to the Netherlands for safe keeping. They were stored at a metal dealer's scrap yard until it was safe to return them after 1930.
All this in order to avoid losing their assets to the Inter Allied Control Commission. When the political climate changed after 1933, the charade and facade was dropped and DWM was 'born again', only to repeat the trick after 1945. Berlin became 'Deutsche Waggon- und Maschinenfabriken' (German railroad car and machine factories), and Karlsruhe became 'IWK'', 'Industriewerke Karlsruhe' which sounded a lot more neutral than the former name. To finish it off, IWK became IWKA in the 1960s when they merged with a company in Augsburg (explaining the A). When IWKA withdrew from Karlsruhe and moved to Augsburg, they chose to adopt the name of the former Augsburg company: Keller und Knappich or 'KuKa' in short. There were a lot of movements in the corporate history, companies sold, bought, merged, etc.. so it's still possible to find remnants of the DWM, IWKA names in other enterprises, even the old logo is sometimes still recognizable.