In summary, 'no statistically significant difference' always refers to 'not ≥ a particular magnitude of difference' and is always associated with the possibility of a type II error.

What is meant by significant difference?

A Significant Difference between two groups or two points in time means that there is a measurable difference between the groups and that, statistically, the probability of obtaining that difference by chance is very small (usually less than 5%).

What does it mean if data is not significantly different?

The "layman's"meaning of not statistically significant is that the strength of relationship or magnitude of difference observed in your SAMPLE, would more likely NOT BE OBSERVED IN the POPULATION your sample purports to represent.