I meant Artificial General Intelligence as that term has been first coined and used in the AI community: the ability to adapt to any new environment or task.
Google's machine learning algorithms can not just correctly classify videos of cats, but can innovate the concept of a cat given a library of images extracted from video content, and no prior knowledge or supervisory feedback.
Roomba interacts with its environment to build a virtual model of my apartment, and uses that acquired knowledge to efficiently vacuum my floors while improvising in the face of unexpected obstacles like a 8mo baby or my cat.
These are both prime examples of applied AI in the marketplace today. But ask Google's neural net to vacuum my floor, or a Roomba to point out videos of cats on the internet and ... well the hypothetical doesn't even make sense -- there is an inferential gap here that can't be crossed as the software is incapable of adapting itself.
A software program which can make changes to its own source code -- either by introspection or random mutation -- can eventually adapt to whatever new environment or goal is presented to it (so long as the search process doesn't get stuck on local maxima, but that's a software engineering problem). Such software is Artificial General Intelligence, AGI.
OpenCog right now has a rather advanced evolutionary search over program space at its core. On youtube you can find some cool videos of OpenCog agents learning and accomplishing arbitrary goals in unstructured virtual environments. Because of the unconstrained evolutionary search over program space, this is technically an AGI. You could put it in any environment with any effectors and any goal and eventually it would figure out both how that goal maps to the environment and how to accomplish it. CogPrime, the theoretical architecture OpenCog is moving towards, is "merely" an addition of many, many other special-purpose memory and heuristic components which both speed the process along and make the agent's thinking process more human-like.
Notice there is nothing in here about the Turing test, nor should there be. Nor is there any requirement that the intelligence be human-level in any way, just that it could be given enough processing power and time. Such intelligences already exist.
"Pass the Turing Test" is a goal, and is therefore a subset of GI. The Wikipedia article says "Artificial general intelligence (AGI) is the intelligence of a (hypothetical) machine that could successfully perform any intellectual task that a human being can."
Your claim that OpenCog can "eventually" accomplish any task is unsupported, is not something that has been "implemented", and is not what is generally understood as what AGI refers to.
In the spirit of "satisficers want to become maximisers" here is a somewhat weaker argument (growing out of a discussion with Daniel Dewey) that "tool AIs" would want to become agent AIs.
The argument is simple. Assume the tool AI is given the task of finding the best plan for achieving some goal. The plan must be realistic and remain within the resources of the AI's controller - energy, money, social power, etc. The best plans are the ones that use these resources in the most effective and economic way to achieve the goal.
And the AI's controller has one special type of resource, uniquely effective at what it does. Namely, the AI itself. It is smart, potentially powerful, and could self-improve and pull all the usual AI tricks. So the best plan a tool AI could come up with, for almost any goal, is "turn me into an agent AI with that goal." The smarter the AI, the better this plan is. Of course, the plan need not read literally like that - it could simply be a complicated plan that, as a side-effect, turns the tool AI into an agent. Or copy the AI's software into a agent design. Or it might just arrange things so that we always end up following the tool AIs advice and consult it often, which is an indirect way of making it into an agent. Depending on how we've programmed the tool AI's preferences, it might be motivated to mislead us about this aspect of its plan, concealing the secret goal of unleashing itself as an agent.
In any case, it does us good to realise that "make me into an agent" is what a tool AI would consider the best possible plan for many goals. So without a hint of agency, it's motivated to make us make it into a agent.