From http://www.it20.info/misc/brokers.htm
This page is intended to be a summary for the various brokering technologies available for the VMware VDI initiative. At least this was the initial intent.
As soon as I started working on this summary two things became clear:
while the idea of the connection broker was initially associated to the VMware VDI initiative, the concept and values of these brokers (or "infrastructure access" packages) has expanded a bit to encompass other client consolidation models such as the more traditional "Terminal Services" model as well as the niche "Workstation Blades" model. Shared Services (i.e. TS / Citrix deployments) are just not death and certainly hosted desktop can't be a good fit for everything either. Not to mention that these connection brokers are or will be able to broker virtual machines hosted also on non-VMware type of hypervisors.
connection brokering is only one piece of the functionality that these "infrastructure access" packages provide. Session brokering is the simple concept of redirecting an end-user to an available OS/application image (either from a pool or his/her own end-user image). As you can see below these packages (at least some of those) provides much more than that. That's the reason for which referring to them as "connection brokers" is kind of limited.
So in a nutshell: what started to be the "VDI connection brokers" are now brokering other things than simply VDI vm's as well as these "VDI connection brokers" are doing more than "simply brokering".