Abstract Existence, Beyond Dimensional Existence, and Higher Dimensional Existence
Higher-dimensional existence is fundamentally a way to define a space a character, being, or structure occupies with four or more spatial axes. This can be four, all the way up to ever-expanding infinite number sets. But all of this still comes down to the object in question can be "defined" as occupying a space through a coordinate system. An object existing purely as an abstract concept (Type 1 Abstract Existence), with no definitive size or spatial occupation within a cosmology, would not qualify for HDE. As there's no higher space it occupies, but rather it exists in a conceptualized state. However, an avatar of a Type 1 Abstract being that occupies reality as a physical form can qualify for HDE, as they can now be defined by a coordinate system.
By a similar notion, Beyond Dimensional Existence (Type 1) exist in a state in which they cannot be quantified by a spatial axis, while not being inherently superior to them in a fashion of qualitative superiority. Because they cannot be defined by a higher-dimensional coordinate system, they would also not qualify for an HDE rating, as there's no way to plot their existence within a spatial coordinate system. BDE Type 2 is slightly different, as those beings have a large relative size beyond spatial constructs, such as being a void that a cosmology is suspended in, but this means that their size inherently does not translate to a spatial coordinate system. Instead, they occupy a relatively larger area of cosmology, which happens to have a subset within itself that is defined by spatial coordinates.
There are possible exceptions to this standard, however. For example, if an Abstract Being occupies the concept whose information can be expressed or defined through spatial coordinates, such as the physical concept of space, then they can have both Abstract Existence and Higher Dimensional Existence at the same time.