Renekton honestly feels more like he is driven by extreme bloodlust or if he is in a constant battlefrenzy.(it doesn't really help that he is literally insane by this moment)
Sure he has a ragebar,but rage doesn't really feel that central to his kit,as it only empowers his abilities and while it isn't completely unimportant to his character,I'd say that it is kinda overshadowed by his insanity
Tryndamere however is motivated by rage,is hinted to be struggling to control it(as Greyor talks about that) and has actual abilities that are based on his rage giving him power(his Q and R who both keep him alive through rage alone),making rage more than just a special resourcebar for him.