What is the difference between "Heat Map Analysis" and "Hot Spot Analysis"?
Are we perhaps using hot spot analysis to get the required relations between features, and then using the results as an input for a heat map?
A good article from ESRI called "Extending your map with spatial analysis" explains and give examples of both.
Another good article, "Heat Maps in GIS", found over on GIS Lounge, shows that these terms can sometimes be used interchangeably.
I think the first paragraph of the article gives a great explanation of the term(s):
Heat mapping, from a geographic perspective, is a method of showing the geographic clustering of a phenomenon. Also known as hot spot mapping, heat maps show locations of higher densities of geographic entities. The ‘heat’ in the term refers to the concentration of the geographic entity within any given spot, not to be confused with heat mapping that refers to the mapping of actual temperatures on the earth’s surface. Heat mapping is a way of geographically visualizing locations so that patterns of higher than average occurrence of things likes crime activity, traffic accidents, or store locations can emerge.
This article explains the difference very vividly: