In a nutshell:
Robohelp HTML is the software used to write your content, generate to multiple different formats (webhelp, chm, AIR, etc) and publish to a final location.
Robhelp Server is a server application designed to run the "Pro" outputs generated by Robohelp HTML. This provides additional functionality not provided by the "vanilla" outputs, such as reports, feedback, and advanced search functionality.
I don't use Server, so perhaps someone else can correct any errors on my part.
Check out Colum's blog - robocolumn.com for more on the difference