HPS have a very high % of red photons and almost no blue so, all other things being equal, you'll get taller plants with an HPS than you will with a white LED.
White LED's have a decent amount of blue in them because blue is good in veg - it keeps plants short, so they're easy to work on, easier to harvest, and because a shorter plant has less difference in secondary metabolites between the top and bottoms areas of the plant. Another benefit of blue photons is that internodal space is reduced so your buds will stack more than if they're not exposed to blue light in veg.
Also, HPS generates red heavy PAR but it also generates heat, and growth rates are higher when there's more heat, up to about 95°.
All in all, plants grown under a white LED will be shorter and more compact than plants grown under HPS.
Below is a photo of the plants in my current grow at day 18.
Below are the light levels for that part of the grow. The XS-1500 is a small LED with a little more blue than most. The "Puck" is a blue LED and the veg light is…a veg light (LED) so, arguably, these plants are a little bit smaller than if they had been grown with just the Viper XS-1500 but they also were getting almost 500µmol which is pretty good light so maybe it's a wash.
All in all, a plant that's 9cm at day 18 sounds about right for a photo but, as
@Bill284 recommends, a grow journal is really helpful.
