It's not fully state owned, it's semi-privatized. You get the worst of both worlds, so to speak.
> Sie [DB AG] befindet sich zu 100 Prozent im Eigentum des Bundes
https://www.bundesfinanzministerium.de/Content/DE/Standardar...
Why they went with an AG in 1993, I don't know.
Typically, on the way, there is also a separation between the "good piece" and the "bad piece" of the company, ie the company that operates the trains (and makes profit out of the passengers etc) and the one that maintains the infrastructure. The state then can sell the profit-generating part of the company to the private sector, and continue operating the non-profitable one itself, so the private capital can enjoy the best of both worlds (having a privatised train company, but still having the state eat up the economic burden of maintaining the infrastructure that the former operates on). Not sure where germany stands in this roadmap, but this is what has happened in other places (and no it did not improve the experience of passengers to any degree).
The issue is one of legal status. In most countries you can be a commercial company or essentially a branch of the government (leaving aside coops and charities).
So in general you have companies (legal status) but they are fully owned by the state, hence "state-owned company". "Privatized" means the government decided to sell most or all the shares to the public.
Counter example is the USPS in the US, which is an agency of the Federal government.
Maybe this is a language barrier issue. Companies organized as AG, GmbH etc. under private law, in opposition to branches of the government or special institutions of public law. This is commonly called "Bahnprivatisierung" in Germany.
The Deutsche Bahn was "privatized" in the sense that it was moved from public law to private law based organization.
It seems "privatization" in english is still a very murky word, even though it does not include this meaning :) https://en.wikipedia.org/wiki/Privatization I'll try to stop calling deutsche bahn "privatized" in english.
This company structure was the result of the neoliberal thinking of having as much free market as possible, with the beneficial side effect of creating many highly payed board chairs for former politicians.
Today, the problems, mainly caused by cutting cost on maintenance, are so close to the surface, that even the most head-in-the-cloud establishment politicians cant spin it anymore, so the new DB ceo (Palla), tasked with "fixing it", came up with a long term plan. For decades, from every side, DB/german governments was critized for not having an articulated goal of the minimum public service that should be provided. The german governments were not directing, so 100% state _owned_ is technically true but obscures the complexity. The former ceo Mehdorn, that started this down trend did exatcly what any short-term-gain ceo would do and is, despite this blatantly failing infrastructure, still well regarded.
Today, one primary goal of this plan to fix it all, is to "reduce delays". Cuting schedules and lines will make this number up too! And so the next round of ceo bonus payments are secured and the shit show continues.
What else could you expect? A solution to fix vital infrastructure and strengthen trust in politicians and governments to cost money?! Haha.
Citation needed.