True, but those are activities that any old gunslinging friends would do. They're just contests. Rivals are people constantly competing against one another and striving to be better (or at least not worse) than the other.

However Woolfwood and Vash? Their only noteable straight-up competitions were the two you mentioned and they were both pretty friendly. (And served as a means to develop their characters and rub Vash's obvious superhuman abilities like bullet deflection in the faces of the audience.)

No, the true rivalry between the two is not of goals, because their goals are the same and they do not want to stop each other nor reach the goal before one another. The rivalry is the paths they take to reach them. Wolfwood is a kind-hearted man but he is incredibly bitter. He is quick to judge and measures the expendability of human life by how many lives are saved by their deaths. He believes in sacrificing the pawn to win the game.

Vash is the complete contrast. He believes there is a path to peace outside of sacrifice. Throughout the series he is incredibly hesitant to even draw his gun on people (the first time he fires it is in episode 5 against the giant's fist. Everything else he did unarmed before then). The truth is that Vash doesn't avoid sacrifice, he simply doesn't mind it himself. A quick glance under his coat and at his bounty show the true nature of his goals. He considers all life sacred and the only life he doesn't mind sacrificing is his own. His health, his body, his reputation, his emotions. Everything is expendable to him so long as he personally owns it.

Wolfwood doesn't sacrifice anything of his own, rather he sacrifices others. That is their rivalry. Idealism vs Realism. Self-sacrifice vs Self-Justification. Ultimately Wolfwood suffers for straying from his path to Vash's whereas, had he kept to his guns (pardon the pun) he would not have had to visit the church.

I enjoy breaking series apart but Trigun is full of chocolate chips!

I really need to re-read R&J...

Are you in 9th grade? Because that was when I read it

Indeed so