IRF vs Autocorrelation function of AR(2)

Will the impulse response function and autocorrelation function of an AR(2) coincide? I say that they will not, because $IRF_{t}(t+k)$ (that is, the effect of a unit shock at time $t$, on the process at $t+k$) will be 1 when $k=0$. However, $corr(y_{t}, y_{t})$ is the variance of the $y_t$ process, and will not necessarily be 1. Thank you.