彼女はクラスのなかで最もかわいい。 彼女はクラスのなかで一番かわいい。 She is the most beautiful in the class. They are the same in this meaning. 最も is more suitable for formal situations, while いちばん is for casual conversations. In other usages, they are not interchangeable. 彼女はクラスのなかで一番の美人だ。 She is the first beauty in the class. マラソンで一番になった。 I got the first place in the marathon.

I think 最も is a formal word and would use for writing (but it is not wrong or anything to use it in a conversation). 1番 is more colloquial than 最も. 例) 私にとって最も大切なのは、家族と友達です。 = 私にとって1番大切なのは、家族と友達です。 = The most important thing to me is my family and friends. They can be used as the same meaning. :)

最も = utmost いちばん = first So they're almost the same, but not quite.