Note: The Higher-Dimensional Existence is for Objects and Entities that are Higher-Dimensional in a proper mathematical sense i.e. the regular 3-Dimensional axis + 1 or more dimensional axis. The following will not qualify for this criteria
1. Viewing 3-Dimensional objects, entities or constructs as fiction; Viewing something as fiction does not mean your body has an extra dimensional axis, as the beings are still portrayed as regular 3-Dimensional beings, they are just 'more real'
2. Holding ontological difference over 3-Dimensional objects, entities or construct; Most times this is a measure of power and will not equate to having an extra dimensional axis
3. Stated to be larger than or contain 3-Dimensional objects, entities or construct; there are numbers of ways fictions portrays infinitely larger than a 3-Dimensional construct but not all of it would mean an extra dimensional axis; being uncountable infinite larger than a 3-Dimensional construct or something similar will mean qualitative superiority as fictions tends to portray it as so, but without further contexts, it should not mean an extra-dimensional axis
4. Stated to be Higher Dimensional or a Higher Plane or a Higher Existence; without further contexts that shows it to be in the virtue of them having an extra dimensional axis to 3-Dimensional entities or objects.
5. Stated to be Extra-Dimensional; the literal meaning of this is an entity or object that comes from outside the regular 3-D space,; this does not mean these entities or objects have an extra dimensional axis in contrast to 3-Dimensional objects, without further contexts.
6. Stated to transcends space or transcend space and time; there are lots of ways a character can transcend without having an extra-dimensional axis or in relation to the geometry of the Object.