[Brighthurst]

As a pedantic native speaker, I'd like to describe the different interpretations I have for these words. Hopefully this explanation illustrates the differences in a more useful way to you than simple ordering. I am not saying that this is exactly what the summary meant for these words, I'm just adding more context:

- Important: Describes that something has high priority, in a general sense. Very broad. Can replace any of the other terms, but is less precise.

- Key: Important in a utilitarian sense. Just like a literal key, using "key" here implies that something is an essential part of a solution to a problem/issue.

- Vital: Important in an ongoing sense. Think of "vitality"," the capacity to live, grow, or develop. We should use "vital" when we mean something is important to do as a habit, to maintain the strength of something.

- Crucial: Another term that is general. Basically "important" but with higher priority. It implies that there is some urgency, gravity, or necessity to whatever is crucial or the matter to which whatever is crucial.