Null Distribution vs Sampling Distribution

Every p-value is measured against the null distribution, which answers what your statistic would look like if the null hypothesis were correct. You get that distribution either from theory (a normal, t, or chi-square model) or from simulation, as in a randomization test. For example, under $H_0: p = 0.50$ with n = 100, the null distribution of p-hat (the sample proportion) is approximately normal, centered at 0.50 with standard deviation $\sqrt{0.50(0.50)/100} = 0.05$. An observed p-hat of 0.60 then sits two standard deviations out, giving a two-sided p-value of about 0.0455.

A sampling distribution describes how a statistic, such as the sample mean, changes from one random sample to the next. For example, taking many samples of 40 students and recording each sample mean builds up the sampling distribution of $\bar{x}$ (x-bar, the sample mean). For the sample mean its center is the population mean $\mu$ (mu) and its spread, the standard error, is $\frac{\sigma}{\sqrt{n}}$ (sigma over the square root of n). This spread shrinks as the sample size grows, so larger samples give more consistent estimates.