So if we don't talk about the score because I doubt it's a S worthy, The grades results from a comparison of everyone playing the same champion on the same role as you. That means if a support janna goes 0/0/20 (all depending on the game but) it can be S worthy. But if a zed goes 0/0/20, when it's compared to the other zeds it's not that good. So if you friend has a different champion than you it's normal you don't get the same rank.
And as you probably know the ranks aren't entirely based on the score. It's also about kill participation, the objectives the length of the game, your creep score and alot of other things. So even if you have a good score you can have a bad rank.