I really really really wish we hadn’t settled on the term “statistically significant”. There’s just too much temptation to elide from “these results show that situation X is statistically significantly different to situation Y” to “the difference between X and Y is significant” to “the difference between X and Y is important”.
Statistical significance is about deciding whether it is reasonable to say that the difference between two things is not due to sampling error. Two things can be statistically significantly different and the magnitude of the difference of no “significance” (in the day-to-day sense) to the situation at hand.
We really should have gone for a term like “robustly distinguishable” or something that doesn’t convey the idea that the difference is important or large in magnitude.