A term structure has a forward curve
So what is it that the short rate model is projecting exactly?
Why is it needed?
How are they different?
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A yield curve is a deterministic function as set and seen at time T=0. One can project any short-term (e.g. 1 mth, 1 wk or 1 day) forward rates from the curve and they are deterministic.
A short rate model only projects the behaviour of the instantaneous short rate (again can be defined as any tenor). The forward rates from this model are generated from the model parameters and might not necessarily match the yield curve.