Is Steins;Gate 0 a sequel to Steins;Gate? If not, what is common between the two and where do they deviate?
Steins;Gate Zero will not be a direct sequel, no. Remember when Okabe stabbed Kurisu and lost his resolve? Only to be revitalized once he received the Operation Skuld D-Mail from his future self? The Okabe in Epigraph and Zero is the Okabe that did not try again after killing Kurisu, the Okabe that gave up and resigned himself to misery.
Steins;Gate 0, in spite of being marketed as the "true sequel" to Steins;Gate, does not take place after the ending of Steins;Gate. Even though it is canonical, it "takes place" just before the ending of Steins;Gate. Although, because it is about time travelling, all events in the narrative are relative, making the concepts of "before" and "after" somewhat meaningless. The events fit in a logical sequence before the "ending" of Steins;Gate, but in a casual sense rather than temporal.
The story between the two is exactly the same upto (and including) Episode 22. It diverges in Episode 23 with the original story being covered in Episode 23: Open the Steins Gate, and the alternate version, a Steins;Gate 0 OVA, being covered in Episode 23(β) Open the Missing Link. As mentioned on the Wikia:
In this story, after killing Makise Kurisu, Okabe Rintarou gives up and accepts her funeral fate.
The main difference between this and the original episode 23 is that this Okabe does not receive the Video-Mail from himself. He will go on to eventually create Operation Skuld and the Video-Mail, helping S;G Okabe thwart world line convergence and successfully avert both Kurisu's death and WWIII in order to enter the Steins;Gate world line of 1.048596% divergence.
TL;DR: In concise, as put on Reddit:
It follows the world where Okabe tried to save Kurisu, but stabbed her instead. It is the worldline in which Okabe doesn't get the "deceive yourself" message from himself, but it is most likely the one that sends that message.