Recently I study some interest rate models.
When I moved on to forward rate models, I see this documents
It said "HJM-type models capture the full dynamics of the entire forward rate curve, while the short-rate models only capture the dynamics of a point on the curve"
What I don't understand is that why short rate model can't not capture the full dynamics of curve? It seems that the only difference in the model is the short rate 'r(t,T)' is substituted for instantaneous forward rate 'f(t,s)'
I mean, the short rate model : $dr(t,s) = μ(t,s)dt + σ(t,s)dW_t$
and the HJM Framework : $df(t,s) = μ(t,s)dt + σ(t,s)dW_t$
So I think the short rate model can capture the dynamics of full term structure. Also any no arbitrage short rate model could make current term structure.
I tried to understand meaning of the above bold&italic sentences with the fixed income securities textbook such as Tuckman, Veronesi.. But it fails.
What I'm misunderstanding now?