An Open Universe is one where the inhabitants can canonically interact with nearly any other species or world, within reason. Note that there is, by definition, more than one separate "open universe" so they aren't all the same one.
A 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 Open Universe in that such rules are generally limiting it to a specific group of the inhabitants, whether by species, class, or other means.
A Semi-Closed Universe is one where the inhabitants can canonically interact with only a few other species/worlds, set by the owner.
A 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-Canon Universe is one where the inhabitants can canonically interact using multiple different universe statuses or multiple different instances of the same universe status - the variations of which would be incompatible.
An Undetermined Universe is one where the universe status is unknown, and interactions are of unknown canonicity in general. This is the default.