Does the use or meaning of "chart" or "map" vary worldwide?
Is there a difference between a chart and map?
Colloquially, I would say not really, by definition yes.
I think the simplest way to put is is:
All charts are maps but not all maps are charts.
: map: such as
a : an outline map exhibiting something (such as climatic or magnetic variations) in its geographical aspects
b : a map for the use of navigators
a : a representation usually on a flat surface of the whole or a part of an area
b : a representation of the celestial sphere or a part of it
c : a diagram or other visual representation that shows the relative position of the parts of something
In other words, maps are outlines of part or all of something while charts contain potentially more information like that needed to navigate or identify airspace. Interestingly according to the definition, if used for navigation its a chart.
I was taught that charts give information on three dimensions of space while maps only represent two dimensional information.
For example, In the VFR sectional chart above, the altitude of various air-spaces, airports and key landmarks are indicated. For nautical charts, the depth of the water is indicated.
Mathematically, (and technically), a Map is any one-to-one or one-to-many association between the items in one set (or list) and the items in another set or list. You can have a map between the items on the surface of the earth and the points on a chart, but you can also have a map between the cities in the country and the individuals who are the mayors of those cities, or between dates, and the events that took place on those dates, or between the colors in the spectrum, and the frequency of the light that generates the color, etc. etc.
Check out This Wikipedia article about "Mapping". In general, the result of any "Mapping" is a "Map" but only those maps that relate geographic or spatial (2D or 3D) points in space to a visual representation of those points are "charts".