Interesting, thanks for posting. Looking forward to further episodes. I remember the D,E,and F train designations when I was in Germany in 1977. IIRC D was Shnellzug (fast), E was Eilzug (express) and F was local trains, I don't recall what it stood for.
I think D was the highest category of fast trains other than the TEE I believe. I think it stood for "Direkt". Later DB introduced InterCity as a brand for its high value trains and partially cannibalized the D category. In doing so, D becoming the second tier trains that for some reason did not warrant the IC designation. From memory D trains always had some form of catering, either from a full restaurant car or a bistro.
The next category down from memory was FD, I think this stood for "Fern-D" (I think), and was used for long distance trains that typically plied secondary routes and served smaller towns, partially overlapping with E trains and partially with D while covering longer distances and offering a higher quality of rolling stock than the former. Mostly these trains would also have catering.
F seems to have been a spin-off from the FD brand with fewer stops, higher speeds and superior levels of comfort.
In later years, maybe the late 1980s or early 1990s, the remaining D and FD trains were rebranded as Inter Regio (IR). The IR brand has since been discontinued, with some becoming IRE (Inter Regio Express). This had to do with political changes that required a clean vertical separation between national trains and local trains, the former being under the command and subsidy of the national government and the latter of regional governments.
E was Eilzug as you say. This equates to semi-express and would encompass trains of a predominantly regional nature that nevertheless skipped stops. Some of these were later subsumed into the IR brand (see above) but were for the most part left as E and later re-branded as RE (Regio-Express) or IRE (see above)
N (Nahvehrkehrszug) were the local trains that typically did all stops. Some are today confusingly branded as RE. In East Germany they were called P (Personenzug)
Some local trains also just had numbers without a preceding letter, so its a bit confusing.
S were and still are the S-Bahn trains (Stadtbahn - in Berlin or Schnellbahn - in some other cities) that did commuter services in and around the major cities and conurbations. In some areas dedicated stock would be used for these trains whereas in others they were just rebranded R trains. Also level of quality and service frequency could vary broadly between locations.
Further categories of note were
AZ -Autozug, train that transported automobiles. This category is discontinued.
NZ - Nachtzug, night trains with sleeping and couchette cars.
There were also quite a few others that appear to have been used only for short periods or reserved for particular trains that somehow didn't fit into any of thee categories. I guess trying to create a full list would be opening a can of worms as many definitions changed over the years.