What was the relationship between 诸葛亮和周瑜？
The enemy of my enemy is my friend.

They may be "friends", but they are still enemies.

They are the minister of two different kingdoms, 蜀 and 吴, they just happen to have a stronger common enemy 魏 so they have to work together to keep each other alive for a while before they get stronger and can defend on their own.

You must have seen that 周瑜 keeps trying to kill 诸葛亮, because he sees 诸葛亮 as a threat in the future when 蜀 and 吴 goes against each other. Obviously when two Kingdoms work together, you can't just kill, that's why he keeps assigning impossible missions to 诸葛亮 so he can use that as an excuse to kill him, but 诸葛亮 never failed and it makes 周瑜 angrier and frustrated. In the end, 周瑜 just ordered his men to kill 诸葛亮 anyways but forseeing that, 诸葛亮 escaped before 周瑜 can catch him.

But on a personal level, 周瑜 just can't stand the fact that there are someone as smart as him and this is what killed him, i think this is the biggest difference between the two, both are equally smart, but 周瑜 died because of "Sickness"(more like Jealousy), he is young after all, if the two have met at a different time, they could have become great friends.

Much like The Republic of China and The People's Republic of China when they were fighting Japan, they have to put their disagreement aside for a while and fight together. After Japan surrendered, they started fighting against each other again.