Both adverbs has the basic meaning "most, extremely". There are also ずいぶん and とても.
So, とても is the first word we usually learn that means "very". Then I learned 最も as a superlative. As for ずいぶん, I understand that it is somewhat subjective to the speaker and carries a feeling of surpise. And now I stumbled across 非常に, how is it different from the other superlatives?