yes, I do know the categories are arbitrary but so is most things in this world so that does not matter?
Except it does matter as understanding how this came about is informative. The categories came to be during the development of 3e, and did so because each of these categories would inform qualities such as number sides to a creature's Hit Dice, their attack progression, skill points, and at what saves they were naturally good. Before that point, creature types/how they related to each other was much more of a 'tag' or 'flag' type scenario (and often an inherently tautological one) -- all creatures affected by a 1e ranger's bonus against giant-type creatures (list included in ranger description) must therefore be 'giant type,' all creatures getting the increased bonus against them from a 'sword +1, +3 vs. ____' must be of that type (and again the sword or monster listings themselves better let you know, or else you will have arguments over whether jackelweres were lycanthropes and if wyverns were dragons).
What this means is that there was an already existing set of creatures developed over ~30 years of proto-D&D and TSR-era D&D that then got retroactively forced into these broad categories (and also that you couldn't just say,
'well, this one doesn't really fit any of the categories, so we'll leave it as an outlier,' since that would fail to provide basic information needed to fill in the creature's basic stats). Almost inherently, there were going to be edge cases where something could have gone in one or the other category (leaving after-the-fact delineation of what makes one qualify for one or the other category murky), as well as one or more 'junk drawer' categories to house all the creatures that just don't fit anywhere else.
I am trying to find the qualities that make aberrations somehow different to monstrosities.
I think you're going to be somewhat disappointed. As others have said, aberrations kinda/sorta are defined by their alien-ness, and that's a pretty nebulous concept (especially when discussing basic biology as much as mindset). It doesn't help that some of
our most iconic conceptions of something being 'alien' are, respectively, an anthropomorphized octopi (real creature), and person in black spandex with a phallic head crest and extra mouth within their mouth (all real parts of creatures), and bodybuilders in fishnets with mandibles (all parts of real creatures). When you get to 'truly' alien things, it tends to become 'made of ____' (stone, goo, motes of light, multiple constituent beings) creatures that usually end up in the elemental, celestial, ooze, or similar groupings.