These meanings are different but sometimes overlap. McCloskey and Ziliak (1996) have a substantial discussion of them. Ambiguity is common in practice, but not hard to avoid. (Editorial comment follows.) When the second meaning is intended, use the phrase "statistically significant" and refer to a level of statistical significance or a p-value. Avoid the aggressive word "insignificant" unless it is clear whether the word is to be taken to mean substantively insignificant or not statistically significant.
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