To explain it better, consider a line chart versus a bar chart. Quantitatively, they display exactly the same data, to the same precision and the same fidelity and visual distortion. However, the two charts do not share the same interpretation. A bar chart places the visual emphasis on the magnitude of each individual data point, and is meant to let you easily compare the value of a data point to any other data point. Meanwhile, a line chart places the visual emphasis on the relative values of successive data point, and is meant to let you estimate rates of change and analyze both where data points not-yet-measured might end up and if rate of change is accelerating or decelerating.

The data that these charts are trying to convey is fundamentally a collection of lines--the possible paths that the eye of the hurricane may take. However, the means of its conveyance is by use of enclosed polygons on the map. These enclosed polygons convey a visual emphasis that all of the contained points share a feature in common. When discussing hurricanes, and given the context of the map, it is very easy to misinterpret that feature to be "this point will see damaging hurricane effects" instead of "this point is between the extremities of the most likely paths of the eye of the hurricane." Note too, how the labels I give are cumbersome: terse descriptions may again mean a label meant to evoke the latter turns out to evoke the former. A more visually accurate representation of the data would be to represent the cone of uncertainty with a collection of lines indicating the mean path and the edges. Perhaps you could add more tracks for more intermediate points to illustrate if the uncertainty is a smooth distribution or if there are weirder clusters (kind of like a spatial violin plot). You could also use varying lightness on the lines to indicate which are the center and which are the edges.