A data structure can be seen as a mathematical object with attendant definition of structure and operations, which can be useful for formal reasoning; or a implementation, an actual executable artifact encoding those structures and operations into a particular runtime, which can be useful to, like, write/run some code.
What you're calling a "logical structure" is not really a thing. It's a sort of outline or mnemonic, usually for the mathematical objects but sometimes the program. It's per se insufficient for either mathematical or practical use. When the outline fails to capture the right details (as it fails here) it's also harmful to anyone trying to understand either view of the data structure.
That's a narrow point of view. It would make minor variations of the same structure different data structures, which is not very useful approach.
Logical structure is the heart of the data structure. It can be understood as the set of invariants maintained by the structure. Those invariants determine which operations can be supported efficiently by some version of the data structure. Layout and encoding choices affect the performance of those operations. The interface determines which operations are available, but it's often a poor match for the actual structure.
The lines between the logical structure, the layout, and the encoding are vague, but the concepts are useful. For example, if two data structures have the same logical structure and layout, they can often share the same serialization format. That implies that there should be a simple but very efficient conversion algorithm between the two, which can prove useful if you sometimes need to support different operations efficiently.
What you're calling a "logical structure" is not really a thing. It's a sort of outline or mnemonic, usually for the mathematical objects but sometimes the program. It's per se insufficient for either mathematical or practical use. When the outline fails to capture the right details (as it fails here) it's also harmful to anyone trying to understand either view of the data structure.