In the Star Trek model we see the input directly limited to the data in the ship and surrounding visual areas (as far as i'm aware)
In the Wally model we see that the input is limited to a single optic/auditory/ect location.
We have a potential network that input can come from everywhere cameras, phones connected to the internet of everything. I think it really comes down to with how we want to interact with AI and how much input should it have to directly interface with us.
Also it's very hard to know even during deployment how accurate an AI will have a grasp on human want and interaction. A lot of people are worried about the 'non-consenting' information potentially available to the net. Very few people, if any, will ever really be able to address it should an AI be created and deployed.
In it, humans are basically treated like pets or toddlers, in that they "do stuff" but they're kind of oblivious to the fact that AI is moving the world forward.
[0] https://en.wikipedia.org/wiki/Person_of_Interest_(TV_series)
As for the Star Trek (TNG) interpretation of AGI, I suspect something like this in the real world would give rise to a kind of "oracle" situation, which creates its own dangerous problems. A system which functions as described only by observing and giving input where asked still has the potential to affect the outcome of events simply by being a reliable predictor.
A paper explaining this concept far better than I would be able to in a HN comment is available here: http://www.aleph.se/papers/oracleAI.pdf
Terminator - To be avoided at all costs (everyone agrees)
Wally - AI does its best to "take care" of us, turning us into infantile, unthinking, pleasure seeking dweebs. The ultimate basal brain utopia. But empty.
Star Trek (TNG) - AI as an assistant to help us fulfill our higher purpose and make us better at being a higher order being. There is no doubt that the ship's computer has advanced AI if you look at the questions posed to it by the engineers and the crew, but it does not impose its "will" upon them. It is an observer until directly asked, even when death is at hand (seemingly).
There is a very good video on YouTube about it, but I can't find it (right now) that explains it in a very accessible way (that's pretty entertaining) with no real knowledge of the underlying functionality necessary. I suggest you watch it. It's great!
EDIT: https://www.youtube.com/watch?v=48mf2QUtUmg&t=949s