The autocorrelation of lag k of a time series is the correlation values of the series k lags apart. The partial autocorrelation of lag k is the conditional correlation of values separated by k lags given the intervening values of the series.
Autocorrelation of lag k is the correlation between Xt and Xt+k where the time series is {Xt}. The partial autocorrelation of lag k is the conditional correlation of Xt and Xt+k given the values of Xt+1, Xt+2, ..., Xt+k-1. There lies the difference.