Keep in mind, those Ninja things have whacky blades, but they differ. One is a “processor” blade, and another is a “blender” blade. I’d venture a guess this is just processed.
Anyway, to your point: the secret to sauces is sifting and filtering. It’s kind of a quick 3 step process:
marinate
heat (heating is somewhat optional in some cases)
blend
sift/filter
If you want a smoother sauce like you’d find in a bottled product, you have a few different ways to go to finish: