What is the difference with these (Figure, Chart or Table and Equation) reference Types. Looking over the available field seems to indicate there is no difference between these reference types. Am I missing something?
Those reference types were added a while ago, and did not become very popular. Word handling of figures and table are more powerful and thus, they have not developed these further, and the tools are rather rudimentary. However, they did not remove the feature, as some people still use it. Anyway, the way word handles the different ref types, at least how it handles the insert Figures and the inserted Tables is different.
paraphrasing the help in Endnote: "Cite While You Write allows you to insert the figure and its caption into a word processing document. Figures will insert into Word as figures. Use the Chart or Table reference type if you want to insert that image as a table in Microsoft Word. Tables are listed and numbered separately from figures in Word. "
Having said all that, I have no idea if it works as advertized as I always insert my Figures and associated Captions (figure titles) and legends (and Tables and association “caption” title) in Word itself, skipping Endnote’s features. In documents such as dissertations/theses, this allows you to manipulate the titles so that you can auto-create the Table of Figures with figure titles and Table of Tables (with table titles).