According to the development plan, 2 full floors but only 3.8m height.

Depending on the federal state. For us, it means that at least 2/3 of the area of the underlying floor must have a ceiling height of 2.2 m.
Search for the building regulations of your federal state.

But now again, I understand two-storey as having the full ceiling height everywhere on the upper floor like a townhouse, or am I mistaken?

The misconception is that two-storey does not necessarily mean townhouse*. A townhouse can also be built as a single-storey structure, just as a two-storey design is not a guarantee for the currently common definition of a *townhouse. The development plan with its individual components generally applies, which an architect can usually cleverly implement into a dream house. The topic is more complex than the amateur classification into bungalow, gable-roof house, and townhouse.

I can understand the confusion of the OP. As far as I have read it correctly, a full story in NRW is reached at a height of 2.30 meters. Thus, two full stories would roughly be UG + 2.30. According to the development plan, however, a maximum eaves height of 3.80 is allowed.

How is that supposed to work?

Are you sure that your definition of full floors is correct? For us, the development plan also shows two full floors and the eaves height is 4.50m, which means that your 2.30m on the first floor would never be achievable here either.

So I have the information from here, but I may have certainly interpreted it incorrectly:

xxx.//recht.nrw.de

Please refrain from hyperlinking; thank you very much!
Construction expert

Yes, it nowhere says that the 2.30m have to be everywhere - it only talks about the "ceiling," which is also present in gable roofs.