Well I would say there is no define answer on it, as covenant shows its possible David maybe made them but also signs of that he didnt and followed a blueprint, and then prometheus goes against it in many ways, and then we have books and also the big differences and we have no reveal of what is the truth yet and most likely wont as Ridley dont seem to get to do the final movie, dead silence on it so far.
For starters we have different names for the type of xenomorphs:
Plagiarus Preapotens: the original aliens
Plagiarus Linesteres: davids alien
Then we have the large difference in design of the creature and eggs:
Starting with the eggs:
Davids alien has petals that goes halfway on the egg, the egg is way bigger than normal xeno egg and very different look. Davids alien egg is different shaped and has a thin bottom while the original aliens egg is flat bottomed and rounder.
The petals on the original egg is only at the top and not going halfway in lenght.
Davids alien egg didnt grow the rotes that the original alien egg does. (in covenant that is supposedly be years old we see has no rotes and just stands on itself on the ground in his basement.)
The facehugger is also way bigger and dont need 8-12 hours to lay its embryo inside a host but just a minute is enough:
The adult form differs quite a lot despite coming from same host: human and I only count alien 1-3 movies here as resurrection wasnt the original alien and avp as well:
Its bigger and different kind of legs and hands.
the backpipes are more merged together than the original ones.
The neck part is hollow on davids while gigers is merged together.
Legs and arms lack the biomechanical look and is more fleshy, much difference in the legs skinn.
the head lacks all tubes and is shorter and the tube that goes horisontaly is longer, it dont have the joints from the jaw that goes to the neck.
Ribcage is very different and not similair at all.
The xenos in aliens who were older had the same body and designs to the hr giger one, just the head and feet was more armoured due to their age and the blades on their forearms, else their body design is identical, while davids isnt.
Then we have the behaviour differences:
David alien is far as clever as big chap and attacked a crane as it though it was an enemy somehow..... And was more easy to trick and far from being the perfect organism as the original aliens was shown as. Also when they bursted out davids alien was transparent and fully formed and didnt need as much time to gestate as the original aliens do.
And if davids alien is the original alien and created them then its still to be explained how their eggs and creatures suddenly change in design to look like hr gigers and james camerons aliens.
Well this is a matter of interpretation and opinion and everything can be changed in the lore, like with a puzzle: enough violence and you can make any piece fit
So those who see David as the aliens creator fine, nothing wrong with it and have it sugested in the movie and lore, same for those of us who thinks he didnt, have things that suggest that being the case too, go with whichever you find best for you
But those differences and what we seen and the novel and expanded materials and names etc to me suggest David made his own version of the xenomorphs and as ridley scott said in an interview: the derelight ship is already on lv-426 and its very old and space jockey fossilised and its been established in the franchise for 40 years, myself isnt a fan of changing things that has been established.
Im pretty much in the same camp as these alien fans, if you have 1 hour and a half of time to spare, quite a good review and bringing up same issues with it all and the franchise as a whole. Gotta laugh at their prediction of the predator movie before it was released and it got as bad as they joked