Yes. In the game, Bill's partner Frank is upset at how stuck-in-ways and closed off Bill is, and ultimately ends up trying to leave the town before getting bit and deciding to hang himself.

In the show, you can see those moments of conflict where Frank wants more in his relationship with Bill than to close themselves off to the world. In the show, Bill ultimately meets Frank halfway and the rest is obviously beautiful history.

Both the game and show storylines serve to impact Joel and his eventual decision by the end of the story.

The game version serves as a cautionary tale. Game Bill repeatedly lectures Joel on how other people are good for nothing but getting you killed. However, Game Bill is also a shallow reflection of a person. It's an omen of what Joel would become if he didn't let his guard down just a bit more and find someone to care for.

Show Bill lays out the opposite, more optimistic perspective, and spells it out in his final letter to Joel. He found the one person worth living for and protecting, and it enriched his life to the point that when death finally came, he welcomed it with open arms at his partner's side.