A "diagram", in contrast to a list, plots two separate, standalone lists/axis/dimensions into relation that previously were unrelated types of data points, so that their alignment or misalignment becomes visually visible. A "map" is not that, it instead tries to accurately or usefully represent data points that are already in reasonable relation to each other, either by nature or deliberate curation. The axis/dimensions of a map are given by the external thing that's mapped, while the axis/dimensions of a diagram can be arbitrarily chosen and plotted, always reasonable per definition as even an "unreasonable" selection of axis/dimensions can lead to the insight that they're not much related, for the diagram is a more universal/general/flexible visualization tool with the decisions of how the data should be presented being an entirely internal, custom, personal matter. A map on the other hand is expected to represent the external subject accurately/usefully, and changing axis/dimensions would destroy the usefulness because the external subject doesn't change accordingly.
I guess we're all aware that the map functions as an abstraction tool (a diagram doesn't and a list not necessarily). There could be said a lot about abstraction as a tool and abstraction tools, but let's just briefly claim that abstraction hides away the more complex details. If it is satellite images of a geographical area of the earth's surface, changing the scale ("zooming out") "abstracts away"/hides the details on the ground for a better overview. The abstraction is not limited to graphical simplification/reduction of the represented subject, it can instead introduce arbitrary elements/symbols/conventions that represent the real thing, especially common if that helps with navigation to further generalize/simplify things that otherwise would naturally differ too much and therefore would be less recognizable (representing the area of a city in unified gray regardless of the color of the roofes, or just as single dots of different or equal sizes).
For a map (or diagram or whatever) to support useful navigation, the axis/dimensions must be concretely defined as a metric that measures data points, otherwise the positioning is arbitrary and doesn't convey any specific meaning visually (it might just as well be a graph, because even a list is ordered). Two data points set into relation to each other define a position on the map, but then, for any second position that's in relation to the first because they are put on the same map, it must be of the same two axis/dimensions and the same scale of the metric, so their "distance" from each other is visually reflected accurately. If not, the map might look pretty, but be less useful as the information it encodes would be misleading. If the axis/dimensions are abandoned as a means of encoding information, additional graphical elements can be introduced that put positions explicitly into visual relation, and not implicitly by the axis/dimensions. Arrows, for example, that connect two positions would be of custom/arbitrary length and have a custom/arbitrary position themselves, as their positioning on the map doesn't encode any specific information other than what's needed for their visual utility (not intersect or overlap, etc.). In such cases, the traditional "map" converges onto graph/network presentation or flowchart-like illustration. The axis/dimensions don't relate to data points and serve merely to span an artificial virtual drawing canvas. To organize and structure such a "map" can become very difficult with increasing complexity, as the axis/dimensions offer no guidance/demand where to put the elements the map is concerned about, and the spacial grouping via nearness and distance doesn't rely on any exact position of the elements, but only on the inclusion, exclusion or "half-clusion" of the elements to a group, while the group as a whole could be at any other position just as well as long as it doesn't collide with another group (the positions of the elements of that other group) by keeping some distance.
If a map isn't used as a passive tool for representing the relation of positions as constructed from the relation of data points along the existing axis/dimensions, but as an active, constructive tool for structuring, the manual, curative positioning of elements can create new data that encodes some information according to what meaning the user wants the axis/dimensions to have. In the most primitive form, it could be spacial grouping of similar, related elements by locating them at similar positions, so the data points that get created/changed in the act of positioning elements encode the information of what elements belong together and are "near" to each other. In a more advanced form, the exact data points of a position are not only adjustable separately for each element and are not only adjustable with a granularity/measure according to the unit of the axis/dimension, but also every element on the map would provide its exact position comprised of the corresponding data points as any diversion from these values for the purpose of visual convenience can, depending on the circumstances, invalidate the map, as it was supposed to be a tool/instrument for those values to be read off from it as its main function. Sometimes it can be legitimate however to "lie" by not representing positions accurately, if the main purpose/usage is less to read these values off for other external use, but to assist the navigation of the external thing that's presented, where the general direction or positional approximation is already good enough as a rough indicator.
Just a side note: we're used to maps that represent geographical areas, but it might be worth investigating maps that represent other things, and if/how these two differ. A map of a hypothetical, imaginary country would still invoke the assumption that it reflects imaginary real geographical locations. For mapping things that have no geographical resemblence whatsoever, like influence/interest spheres of a group of people, a difference between map and diagram might be that maps offer the unique feature of "coverage" of an area on a canvas, while the canvas of a diagram is limited to data points/positions and lines. This would mean that lists/data points are not sufficient as a source for the axis/dimensions of an area map, instead, a non-overlapping polygon (of straight connection lines that form the boundary or curved lines, if there's data to support it) made out of positions (that are made from the relation of two datapoints set into relation from the list/axis/dimension) is needed, the polygon is basically constructed from a grouping of positions, and a position is a multi-dimensional group of atomic data points.
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