Hi Paul,
if you connect via Browser directly to the ESXi Host than you use the "Host Client".
The WebClient is the Flex(Flash) based Client which is used when you connect to the vCenter with your Browser. The new HTML5 Version which is also offerd by the vCenter is "vSphere Client".
As the others already answers .. you need the vCenter which brings the VMware Update Manager into the game and indeed you havent use the "Web Client" yet.
Regards
Joerg