a trill is simply just an arrangement of notes played in a specific order, some people class it as playing a mini scale. Mathematically there is something like 268,435,455 different scales, which are impossible to learn in a lifetime, fortunately we only need a few of them.
the frustrating thing i find with trills and embellishments for that matter, is you can play embellishments in the style of different famous sax players and they sound different. So if your trill sounds slightly different, that’s ok, because that’s your style and the way you play a trill and if you become famous, people will recognise you from the way you play a trill.
lots of meaningless waffle, sadly true.