I don’t think it matters very much as the grade alone is insufficient description of the coin. So I think GEF, no wear, weak strike means the same thing as UNC, weak strike. It might even be beneficial for a dealer to use the former as it gives an impression of a stricter standard.
As has been pointed out previously, the Spink definition of “fine” is “a coin that exhibits considerable wear on the raised surfaces of the design, either through circulation, or damage perhaps due to faulty striking.” Hence, I assume that some would give a lower grade for a coin that is particularly weak strike.
Another reason why I don’t think it matters is that most of the grading terms are, misnomers anyway. “Good” means the opposite of what it is reality. “Fine” isn’t fine. “Extremely” as in extremely fine is not extreme. The majority of coins described as “uncirculated” have probably been circulated for however brief periods of time. Even the term “mint state” doesn’t quite work as no one can be certain if the contact marks were in fact caused by circulation or not. TPG have no issues describing toned coins as “mint state” even though coins are of course not toned when there were just minted.
In short the coin is the same regardless of the grade assigned by an individual. Personally, I think the phrases like “fully lustrous”, “particularly well struck”, “very few bagmarks”, “minor hairlines” etc are more helpful providing they are given in good faith.