There is only one legal case that is not a gift, sale, inheritance (including anticipated inheritance) or similar. That is the transfer of a property/real estate between spouses without consideration. This is not a gift. All other legal transactions can be classified under the cases I mentioned.
In the mentioned case, one partner "sells" their share to the other partner. Instead of paying money, debts are assumed.
Transferring a property is simply a common term for a variety of possible legal transactions.
First of all, thank you very much for the answers and suggestions!
Summary:
I am buying the house and the "purchase price" would be the assumption of the loan (halved, since there are two of us on it). Everything through a notary, as prescribed.
How is the amount of real estate transfer tax calculated then? Does the house have to be appraised or will the tax office accept the figures mentioned? In our case, they come quite close to the actual value.