That is a difficult question to reply with a single answer.

There are unit trains belonging to particular operators, e.g. a Hupac train from Rotterdam to Italy or the Ambrogio container shuttle from Germany to Italy. Those trains would normally be composed of cars operated and assembled by the operator.
There are also unit trains that belong to particular companies, e.g. a Petrol train from Germany to Switzerland, where the consist would be composed of cars leased by the oil company or refinery, which could include cars from multiple operators or lessors.
I have many "Wascosa" tank cars, but also have GATX, VTG and others. Using those cars, I can put together a consist of generic cars that could make up almost any modern oil car consist. If I want to be more specific, I can throw in my various cars labelled for "Petra-Plus" or other companies, which transform the consist from generic to a specific oil company.
Getting back to your specific query about DB Cargo and AAE cars. Let's say DB Cargo is pulling a container train from Hamburg to Munich. That train might include DB Cargo or Railion Sgnss cars. DB Cargo might also have leased additional cars from AAE, which might be used in that consist. It could also happen that DB Cargo is contracted to haul a container train from Port to destination, but the train belongs to the shipping company (Samskip, MSC, etc) and that company has leased cars from various operators (VTG/AAE, Wascosa, Touax, Ermewa, etc). If the train required additional cars for a specific run, they might ask DB Cargo to provide those additional cars.
The problem is that Maerklin has released AAE Sgnss cars from operators including Cemat, Locon, BoxXpress. It might be possible to find AAE cars in various consists, but once a car has been leased to an operator, it is unlikely that that car would be used by other operators. I would not expect to find a Locon car and a BoxXpress car in the same consist unless the two operators were sharing a route. Some companies, like Hupac, are in business both as operators as well as fleet leasing, so it might be possible to find Hupac cars both in Hupac trains as well as in use by other operators.
I managed to find two 47081 sets, a few 47097 cars and along with my 474XX cars, can assemble a Hupac train, which I can use with a number of assorted loads.
(Vos Logistics, Hangartner, Samskip/Geest, etc). With a few additional cars from other makes, I can make it a typical Hupac train.
I took a few Cemat 47095 to make a MSC train even though those cars might not be the right ones for the run through Switzerland. I also have the 47070 (Crossrail) and 47096 (SBB Cargo) sets to make a SBB container train. I don't know how common it was to find SBB Cargo cars with Crossrail loads though. I think that Crossrail had cars leased from AAE.

As far as DB services, I remember seeing photos of the "Red Train", which was a DB Cargo/Railion container train which used to run on the Gotthard from Germany to Italy and back.
DB cars were also standard on the "Winner Transport" train on the same route. I suppose that these trains could have had a mix of DB, DB Cargo and Railion material.
My Samskip train has cars registered to Railion NL and RailReLease NL as Maerklin did not make AAE/ERS cars.

I wonder if Maerklin would not be better off simply making the models for the leasing company (VTG/AAE, Wascosa, Hupac, etc) without labelling the cars for a specific lessee, which would mean that it would be easier to use the same car in various consists.

If you have a few left over cars that don't fit a specific consist, those can be added to a local or mixed freight, made up of all kinds of cars that could be found between freight hubs and local delivery destinations.

I hope that this info helps. I am sure that some people ignore the small markings and just run whatever they feel like. After all, in this hobby, we have to use our imaginations a little too.

Regards

Mike C

To add some interest for ongoing thoughts, I have compiled a list of container shipping lines ranked by size.
This comes from various sources, mainly Wikipedia.
It gives some idea of the ratios of cargo likely to be seen on rail.

1.
A.P. Møller – Mærsk A/S (Denmark)
2.
MSC Mediterranean Shipping Company S.A. (MSC) (Switzerland)
3.
China COSCO Shipping Corporation Limited,
4.
CMA CGM S.A. (France)
5.
Evergreen Marine Corporation (Taiwan)
6.
Hapag-Lloyd AG (multi-national)
7.
Orient Overseas Container Line (OOCL) (Hong Kong, China)
8.
Hamburg Südamerikanische Dampfschifffahrts-Gesellschaft A/S & Co KG – Hamburg Süd (subsidiary of Maersk)
9.
Yang Ming Marine Transport Corporation (Taiwan)
10.
Nippon Yusen NYK (Japan)

Kimball