No. There is not. There are many definitions of statistically different.

It is necessary is to state what difference is important to the question posed and how this difference affects the outcome..

No. It is the population means that are equal with high probability. The sample means are, of course, not equal. Best wishes, David Booth

I think you need to read about the idea of hypotheses testing, where in hypotheses testing we test the equality of population means using samples data and probability theory. Samples means are not our objectives, but populations means are.

@ Joseph L Alvarez ,

There are many definitions of statistically different.

But, is there any definition of statistically equal ?

If the definitions of statistically different are mentioned/explained then it may be possible to construct the definition of statistically equal.

@ David Eugene Booth ,

Does

" the population means are equal with high probability "

imply that the population means are equal ?

" Equal with high probability" does not logically imply "Equal".

Therefore, the problem is how to whether equal or not equal.

@ Ayman Amin ,

In hypothesis testing, the null hypothesis of the equality of population means is not rejected if the difference among them is found to be insignificant. Thus, the insignificance of difference is regarded as equal here.

However, logically insignificance of difference does not imply " equal " but zero difference implies " equal" .

This may lead to the necessity of statistical definition of equality as I feel.