What is the difference between "Agreed." and "I agree."?

What is the difference between "Agreed." and "I agree."? Thank you.

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I used "agreed" a bit, partly due to a coworker, but it's quicker than "I agree", its own thought (unlike "Same"), and it actually elevates the discussion in that using it says--to me--that I am treating that to which I agree as a formal proposal, and I am jointly adopting it ("It is agreed that <what the OP said>").