Sampling Variability vs Sampling Error

Two random samples from the same population almost never give the same value, so a sample statistic bounces around the parameter it estimates. For example, two random samples of 50 students from one school might give mean GPAs of 3.12 and 3.05 with nothing wrong in either sample. Sampling variability shrinks as the sample size grows, because the sampling distribution of the statistic gets narrower. Bias behaves differently: it is a systematic push in one direction, and a larger sample does not remove it.

Sampling error is not an error in the everyday sense, and the name is what trips students up. Even a flawless simple random sample produces a statistic that misses the parameter, purely because a different random sample would have landed somewhere else. If the true population proportion is $p = 0.50$ and one random sample of 100 gives $\hat{p} = 0.46$ (p-hat, the sample proportion), the sampling error for that sample is $0.46 - 0.50 = -0.04$. Sampling error shrinks as $n$ grows, but errors from bad methods, such as undercoverage or nonresponse, are non-sampling errors and a bigger sample will not touch them.