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Are they same?

I know they are absolutely different due to the different concept, but a paper said they are same. Is it true?

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    $\begingroup$ Your question is self-contradictory. $\endgroup$ – mkt - Reinstate Monica Mar 26 '18 at 22:23
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    $\begingroup$ Please give a quote and a full reference (if possible with a link as well) so we can see what was said. Perhaps it was a reference to linearity of estimators rather than linearity of relationships between variables; the difference may be crucial to a correct understanding of their point. We need more context. $\endgroup$ – Glen_b Mar 27 '18 at 0:18
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    $\begingroup$ @Glen_b: Good point! Even if the said paper mentioned the linearity of the estimators, that concept refers to how the estimators were obtained. In contrast, normality of the estimators refers to how the vales of the estimators are distributed across many repetitions of a study/experiment under similar conditions. So the two concepts can't possibly be the same, unless I am missing something obvious. $\endgroup$ – Isabella Ghement Mar 28 '18 at 21:36
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The two concepts apply to different entities, so they can't possibly be the same.

We say that a relationship between two variables is non-linear (that is, it is NOT linear). We might also say that the effect of one variable on another variable is non-linear in nature.

On the other hand, we say that the distribution of a variable is non-normal (that is, it is NOT normal).

So non-linearity applies to relationships or effects. Non-normality applies to distributions.

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