I see, seems a bit counterintuitive to me, I feel like they should both act the same, but adding a group and changing it to seamless does the trick, thanks!
Of course, except if I were to put the Link field inside a standard Group field, now they could both have the same slug. And I could retrieve the data of both fields like so:
get_sub_field('name_of_clone')['link'];
get_sub_field('link');
So logically, I should be able to do the same inside a clone that is set to act like a group, no?