A heat map is a graphical representation of data where the individual values contained in a matrix are represented as colors.
Apparently, a geographic heat map is only one kind, and this is the only kind relevant to me. Cartography is about geographic maps. In cartography, I often distinguish between topographic and thematic maps.
A thematic map is a type of map or chart especially designed to show a particular theme connected with a specific geographic area.
In thematic cartography, we can at least distinguish between types of thematic maps: statistical, color, choropleth, isopleth, dasymetric, point-symbol, and so on.
How is a geographic heat map any different from a colored statistical thematic map?