Until today, I had never seen an episode of Angel; the Angel that I knew was solely Buffy-based. While we pointed out some differences between Angel and Buffy in class today (more adult situations and so on), I have been thinking a bit more about how Angel, as a show, works with Buffy, particularly since the character of Angel was deemed worthy of his own spin off.
Angel's place within Buffy the Vampire Slayer is indelible. He's Buffy's first big love and proof that vampires can maintain some humanity (although there was that pesky curse). Still, Angel goes through major changes on the show, always in between the worlds of the ultimate good-guy or regressing into his soul-less vampire ways. Then, he simultaneously leaves Buffy/Buffy -- the relationship and the show.
The show Angel, however, allows the character to be presented more fully; he's on a mission to make things right with himself and his past. Doyle, the sidekick character, introduces the theme of atonement by saying "Well, we've all got something to atone for" when he acknowledges Angel's checkered past and motivations for wanting to help Tina. Aside from the theme of atonement in the context of the episode, I think that Angel as a whole atones for Angel's departure from Buffy's life (and her show). Somehow, Angel getting his own show makes it feel a little bit better that he's no longer on Buffy as the brooding on-again off-again love of her life. I think Whedon takes Angel's best qualities and is attempting to develop them with Angel to help loyal Buffy fans (and especially Team Angel fans) tune in to the new show. It's all Angel, all the time!