I know that there are comics and video-games with crossovers between the two franchises, but in canonical reference, do they really co-exist?
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The simplest answer is no. Although the world of Terminator isn't mutually exclusive from the world of Robocop (as evidenced by the comic + video-game crossovers), there is no canon reason to assume that one is set in the same world as the other.
On top of that, the film Robocop seems to be set between November 2043 and February 2044 whereas "Judgement Day" in the first couple of Terminator films occurs sometime between June 2005 and October 2011.
On a more positive note, the original Robocop film trailer had the Terminator theme running in the background so there's been some slight crossover, if only because the film shared a distributor...
No, they are not in the same universe.
One big difference is - Skynet appears to be entirely machine driven, as in AI gone nasty on it's creators.
In Robocop, it was evil corporations run by humans calling the shots.