a). Correct. An aggregate can be defined as a consistency boundary. Things outside of that boundary, such as other aggregates, are those entities which can be acceptably updated as part of a subsequent transaction. This is eventual consistency.
b). Often times, temporarily stale data is acceptable from the business perspective and should be discussed explicitly. Also, inconsistency actually manifests in places typically regarded as consistent. For instance, as soon as you request data from some service and receive it, the data has the potential to be inconsistent unless there is an ambient transaction. If the requested resource is remote, the transaction will have to be distributed and thus subject to all of the pitfals of 2PC.
Take a look at Udi Dahan's article on Event-Driven Architecture which discussed eventual consistency from the business perspective.