Could someone show me the difference? I do not know how to distinguish the usage of dimension and dimensionality when saying something is high-dimensional.
Dimension is a noun.
A measurable extent of a particular kind, such as length, breadth, depth, or height:
Length is a dimension in this system.
Transforming a noun into an adjective with -al denotes relating to or kind of:
The noun dimension + -al produces the adjective dimensional:
relating to dimension.
The Y axis is a dimensional reference for length in the system.
Forming a noun with -ity denotes a quality or condition:
The adjective dimensional + -ity produces the noun dimensionality:
the condition of relating to dimension.
An additional axis changes the dimensionality in the system.
The noun dimension refers to the actual thing.
The adjective dimensional refers to relating to the actual thing.
The noun dimensionality refers to the condition of relating to the actual thing.
Changing what is up or down into what is left or right is a change in dimension: the vertical dimension is changed to the horizontal dimension. Changing what can be drawn on a sheet of paper to what needs also height above the paper to be properly displayed is a change in dimensionality: two dimensions is changed to 3D, with 3 spatial dimensions. A higher order dimensionality requires additional information to specify the locations of things.
"Dimension" refers to actual, three-dimensional measurements, and "dimensionality" refers to perceived dimensions, represented two-dimensionally. For example: dimensionality within a pattern printed on fabric. (Actually, you could use "dimension" for both descriptions, but "dimensionality" implies that it is an illusion.