Is the Phrase “Critically Important” Redundant?

“Critical” and “important” mean the same thing.

Therefore, to use the two terms together — “critically important,” as many people do — seems redundant.

Why not just say “critical” or “vital”?

I suspect the answer is because “critically important” is emphatic in a way that “critical” by itself is not. “Critically important” sounds more urgent and more serious than “critical.”