In parameter confidence intervals, one estimates population parameters; if one wishes to interpret this as prediction of the next sample, one models "the next sample" as a draw from this estimated population, using the (estimated) "population" distribution. By contrast, in predictive confidence intervals, one uses the "sampling" distribution of (a statistic of) a sample of "n" or "n" + 1 observations from such a population, and the population distribution is not directly used, though the assumption about its form (though not the values of its parameters) is used in computing the sampling distribution.