Critical Value vs Standard Error

A critical value marks how far out on a distribution you go to capture a chosen probability. For a confidence interval it is the number of standard errors that brackets the middle C% of the sampling distribution. For example, a 95% confidence interval for a mean using the normal model uses $z^* = 1.96$, because 95% of the standard normal curve lies within 1.96 standard deviations of the center. With small samples and unknown population spread you instead read $t^*$ from the $t$-distribution using the degrees of freedom.

The standard error plays the same role for a statistic that the standard deviation plays for raw data, and it gets smaller as the sample size grows. For example, the standard error of a sample proportion is $\sqrt{\frac{p(1-p)}{n}}$ (the square root of p times one minus p, divided by n). For a sample mean it is $\frac{\sigma}{\sqrt{n}}$ (sigma, the population standard deviation, over the square root of n). A smaller standard error means the estimate is more precise, which narrows a confidence interval.