How is the Western Knight’s code of Chivalry like the Japanese Samujai’s code of Bushido?
Because neither of them involves running a bicycle into a penguin.
Yikes almighty. I’ll toss up a quick answer here, and others will be along eventually to post the War and Peace version. There’s not a lot of crossover; it’s easier to compare the overall, big picture differences between the two.
The medieval knight was concerned about maintain his station in society. How he conducted himself and what he did, the expenses he incurred and the risks he took in combat, were to properly reinforce and protect his station. If he died in combat, he died trying to protect what was his.
The medieval samurai was concerned about obeying his lord. He conducted himself and did what he did out of honor and respect to his lord, and the various risks he may have taken would be either to protect his lord or get stuff for him. If he died doing what his lord commanded, his family would be taken care of by his lord. There was no greater honor for a samurai than to die in service to his lord.
Samurai being a term which means “servant” hence the samurai unquestioningly serving their lord. Anyone could be a bushi, a warrior, even a ronin. Bushido roughly translates into “way of the warrior”.
You’d think I’d be the expert on this, but you’d be oh-so wrong. 
As far as I can tell, same concept: different cultures. Ethilrist sums up the main difference pretty well, but it should be noted that there was quite a bit of “loyalty to the king or lord” involved in chivalry, as well as “expand and extend your own wealth and reputation” in the bushido code.
So while the focus may shift a litte, the basic ideas are still the same.