In HJM model (framework), the drift of the forward is determined by its diffusion coefficient:
$$ \mu(t,s) = \sigma(t,s)\int_t^s \sigma(t,v)^Tdv $$
My understanding, is that the change of measure under Grisanov theorem for continuous-time semi-martingales only affect the finite variation part (i.e. drift for HJM). Thus, if we start with an SDE under a risk-neutral-measure $Q$
$$ df(t,s) = \mu^Q(t,s)dt + \sigma(t,s)dW_t^Q $$
and the change to the real-world measure $P$ changes this to
$$ df(t,s) = \mu^P(t,s)dt + \sigma(t,s)dW_t^P $$
does this then mean that $\mu^Q(t,s) = \mu^P(t,s)$ since they are both functions of $\sigma(t,s)$?