What is the difference between the discounted mean term and the volatility of interest rates?

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So I think the ActEd Notes define the DMT and Volatility as the same. But in reality, the DMT is a function of the force of I interest (delta) while Volatility is a function of interest rate (i).

The difference between the two comes when you take the first derivative of the present value. For the DMT, you take the derivative with respect to delta whereas for Volatility, you take the derivative with respect to the i. This results in the following relationship:

Vol (i)=vDMT(delta)

The above relationship is derived using the chain rule.