(Caveate: I'm newer to the specifics of National Statistics' Output Area geography than you are.)

From both the BoundaryViewer and output-areas-explained links you provide, I reach the same conclusion you do: there is a simple hierarchical relationship with Lower Layer Super Output Areas (LSOA) nesting inside, and filling, Middle Layer Super Output Areas (MSOA).

The SOA layers form a hierarchy based on aggregations of Output Areas (OAs).

 

The two layers of SOA, with areas intermediate in size between census Output Areas (OAs) and local authorities, each layer nesting inside the layer above.

Here's another quote, from a third reference (neighbourhood-statistics-geography-glossary):

Hierarchy

This refers to the different geographic hierarchies for which data are available on the website. The most important of these are the Statistical Geographic Hierarchies (Output Area - Lower Layer Super Output Area - Middle Layer Super Output Area - Local Authority - County ...

(Caveate: I'm newer to the specifics of National Statistics' Output Area geography than you are.)

From both the BoundaryViewer and output-areas-explained links you provide, I reach the same conclusion you do: there is a simple hierarchical relationship with Lower Layer Super Output Areas (LSOA) nesting inside, and filling, Middle Layer Super Output Areas (MSOA).

The SOA layers form a hierarchy based on aggregations of Output Areas (OAs).

The two layers of SOA, with areas intermediate in size between census Output Areas (OAs) and local authorities, each layer nesting inside the layer above.

Here's another quote, from a third reference (neighbourhood-statistics-geography-glossary):

Hierarchy

This refers to the different geographic hierarchies for which data are available on the website. The most important of these are the Statistical Geographic Hierarchies (Output Area - Lower Layer Super Output Area - Middle Layer Super Output Area - Local Authority - County ...

(Caveate: I'm newer to the specifics of National Statistics' Output Area geography than you are.)

From both the BoundaryViewer and output-areas-explained links you provide, I reach the same conclusion you do: there is a simple hierarchical relationship with Lower Layer Super Output Areas (LSOA) nesting inside, and filling, Middle Layer Super Output Areas (MSOA).

The SOA layers form a hierarchy based on aggregations of Output Areas (OAs).

The two layers of SOA, with areas intermediate in size between census Output Areas (OAs) and local authorities, each layer nesting inside the layer above.

(Caveate: I'm newer to the specifics of National Statistics' Output Area geography than you are.)

From both the BoundaryViewer and output-areas-explained links you provide, I reach the same conclusion you do: there is a simple hierarchical relationship with Lower Layer Super Output Areas (LSOA) nesting inside, and filling, Middle Layer Super Output Areas (MSOA).

The SOA layers form a hierarchy based on aggregations of Output Areas (OAs).

The two layers of SOA, with areas intermediate in size between census Output Areas (OAs) and local authorities, each layer nesting inside the layer above.

Here's another quote, from a third reference (neighbourhood-statistics-geography-glossary):

Hierarchy

This refers to the different geographic hierarchies for which data are available on the website. The most important of these are the Statistical Geographic Hierarchies (Output Area - Lower Layer Super Output Area - Middle Layer Super Output Area - Local Authority - County ...