For many VMware Tanzu GemFire discussions, you need to understand the difference between local and remote membership and caching.
Discussions of Tanzu GemFire membership and caching activities often differentiate between local and remote. Local caching always refers to the central member under discussion, if there is one such obvious member, and remote refers to other members. If there is no clear, single local member, the discussion assigns names to the members to differentiate. Operations, data, configuration, and so forth that are "local to member Q" are running or resident inside the member Q process. Operations, data, configuration, and so on, that are "remote to member Q" are running or resident inside some other member.
The local cache is the cache belonging to the local member. All other caches are remote, whether in other members of the same cluster or in different clusters.