The first thing is if B cant live without A and there are some invariants involved, to me A is an Aggregate root, with B being an entity that belongs to it.
Aggregate roots represent a real world concept and dont just exist for the convenience of modification. In many of our applications, we don't modify state of our aggregate roots once created - i.e. we in effect have immutable aggregate roots. These would have some logic for design by contract checks/invariant checks etc but they are in effect anaemic as there is no "Update" methods due to its immutability. Since the "blue book" was written by Eric Evans, alot of things have changed, e.g. the concept of NoSql database have become very popular, functional programming concepts have become very influential rising to more advanced DDD style architectures being recommended such as CQRS. So for example, rather than doing updates to a database I can append (i.e. insert) instead. This leads to aggregates no longer having to be "updated". This leads to leaner anaemic types but this is what we want in this context. The issue before with anaemic types was that "update logic" for a given type was put elsewhere in the codebase instead of being put into the type itself. However if you do not require "update logic" in the first place then you dont have that problem!
If for example there is an Order with many OrderItems, we would create an Order aggregate root and an OrderItem entity. Its a very important concept to distill your domain to properly identify what are aggregates, entities and value types.
Then creation of domain services, repositories etc just flows naturally. For example, aggregate roots and repositories are 1 to 1 i.e. in the example above we would have an Order repository and not have an OrderItem repository. That way your main domain concepts are spread throughout your code in a predictable and easy to understand way.
Finally, in your specific question I would not treat them as the same entities. In one context, you seem to need modification logic - in the other they you dont - they are separate domain concepts to me.
- In context where modifications are made: A=agg root, B=entity.
- In context without modifications: A=agg root (immutable), B=entity(immutable)