group-by: question

Hi,
I don't understand the functionality of argument [key] in procedure [group-by].
If I understand it correctly,
this functionality always can be incorporated in argument [same?]:


(group-by
 (lambda (x) (modulo x 3))
 '(1 2 1 2 54 2 5 43 7 2 643 1 2 0))

(group-by identity 
'(1 2 1 2 54 2 5 43 7 2 643 1 2 0)
 (λ (x y) (zero? (modulo (- x y) 3))))

An explanation of the functionality of argument [key] would be very welcome.

Thanks, Jos

PS.
Today I came across procedure [group-by].
Up to today I used my own version of [group-by]
without [key]-argument (called [eqv-classes]).
In order to avoid duplicate code,
from now on use [group-by]
but always with [key] = [identity].
Jos

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