We are also struggling with the word Context. The thought was "a Connector is a dumb pipe and it needs a Context in which to run" (e.g. the auth credentials, etc.). Not perfect, and possibly something that will change in the not too distant future, but it works for now.
The whole project is still very young, but we are incredibly excited about all the cool apps that will be created on top of it.
It's not really a separate pipe, its's simply the bits of information that tell the dumb pipe where/how to run. For example, the Google Docs connector knows generically how to connect to a hypothetical person's Gdocs account, but the auth credentials provide the information that is required to connect to a real person's account.
A "smart pipe" is actually a lot more like the Collections. They bring data in from sets of similar Connectors (dump pipe) and collect, de-dupe, and normalize it.
The whole project is still very young, but we are incredibly excited about all the cool apps that will be created on top of it.