Standard deviation is just the average distance of each value in a dataset from the dataset’s mean. In a normal (or near normal) distribution (tied to the central limit theorem), then 1, 2, and 3 standard deviations from the mean cover ~68/95/99.7% of the data. So by nature >= 2-3 standard deviations away from the mean implies <= 5% chance of occurrence.
And IQR is just the middle 50% of the ordered data. Replacing a dataset’s tails with anomalies will skew the mean and increase the standard deviation, but not affect the IQR (or even median).
There’s nuances to all of this, but that’s the gist of it.