Long time fan of the book here. Terry loved Good Omens and always imagined it as a romantic comedy. As Neil will say, it was always supposed to be a love story of sorts. When he wrote the show version, he basically made that canon, to an extent. There are a lot of differences, so much so the show is like a different take on the story entirely.
Here is the real tragedy though, Terry died before he could make the live action version of one of his favorite stories and left it as his dying wish that Neil make the show the way he always wanted it to be. He was even in the middle of writing the sequel of Good Omens where Az and Crowley get a cottage in south downs together and Gabriel is leading the armies of heaven against earth and hell. Neil took some of those ideas into the show.
Now Good Omens is topping book charts and has Emmy nominations. Poor Terry never got to see everyone love his story the way he did. Fucking tragic.