An Accessible World (formerly "Open Universe") is one where the inhabitants can canonically interact with nearly any other species or world, within reason.
A Restricted World (formerly "Semi-Open Universe") is one where the inhabitants can canonically interact with nearly any other species or world, restricted by rules set by the owner. This is different from an Accessible World in that such rules are generally limiting it to a specific group of the inhabitants, whether by species, class, or other means.
An Isolated World (formerly "Semi-Closed Universe") is one where the inhabitants can canonically interact with only a few other species/worlds, set by the owner.
An Inaccessible World (formerly "Closed Universe") is one where the inhabitants cannot canonically interact with species other than the ones native to their world, universe, or in some cases, the specific area of their world they are in.
A Multi-Universe World is one where the inhabitants can canonically interact using multiple different world statuses or multiple different instances of the same world status - the variations of which would be incompatible.
An Undetermined World is one where the world status is unknown, and interactions are of unknown canonicity in general. This is the default.