You could be clearer by answering the question that I ask now for the third time:

Do you think it’s reasonable to translate Warenhaus as warehouse?

now,

[they] are both types of cheesecake on account of both being cakes made out of cheese.

So, if you take the keys (i.e. the tables describing the meaning of symbols) of several maps and paste them onto a board, is what you have a keyboard? If your keyboard is coloured black, can you describe it as a blackboard?

The fact is that compound words have their own meanings, separate from the meaning of their components. Football refers not only to the ball, but the game it is played with - a completely different thing. If you created a spherical object out of rabbits' feet, it would not be valid to call it a "football" except as some kind of poetic irony.

So too with cheesecake. Cheesecake is a word in its own right; it is not valid to simply analyse it as meaning "any kind of cake made with any kind of cheese." You have to look at its actual usage in practice.

• These cheese oatcakes are not cheesecakes
• If for some reason someone started making soap with cheese as an ingredient, a cake of that soap would not be a cheesecake
• an experimental sponge cake that incorporated a little parmesan to give an interesting flavour would not be a cheesecake
• A savoury pancake topped with cheese is not a cheesecake