Let me try to answer this.
The short answer: it’s the same that differentiates a JRPG and a western RPG. Well not the same, but it’s the same sort of differentiation. And it’s not purely on how story is structured, but the mechanical core feels very different.
The long attempt at an answer: The core is the same, tactical turn battles. But in general non-TRPG tactical games rely on less, but more nuanced systems, while TRPG go heavy on the layering of several, not-so-complex systems on top of each other. They also tend to offer a lot of specific and discrete ways to break such systems.
So, something like Battle brothers has like a myriad of stats that they layer into a combat system everybody uses. Some skills do add rules or change the system, but many (most?) add specific damage in specific situations, buffs, etc. There’s not a lot of class-based differentiation and the starting stats serve to differentiate progression and utility between characters.
A typical TRPG has less stats, but what feels like a million classes, each doing something relatively unique (special spells, attacks, even full on mechanics and systems relative to any single class). Same with skills, many of them do add new mechanics (recruit enemies! Counterattack -it’s a skill and not a system-wide combat variable- etc). To the extent many TRPGs meta games are about using the many systems to break the game. Those aware enough offer challenges that require breaking the game (or insane grinding) to defeat.
In a way. Battle Brothers would be more of a TRPG if it allowed you to recruit and play as many of the monsters with special mechanics.
So TRPG are about many discrete systems and skills that do unique things and interrelate, while western tactical games are more about a more solid and deeper core system that allows differentiation within it but less variation and less out of the box stuff.
The above doesn’t always hold true, but I think it’s the core of the flavor differences. Of course specific games can walk along a grey area between the styles.
This approach has the advantage of making something like Triangle Strategy a straight up TRPG even with the customization simplification. In that game every single character is unique. Mechanically unique. In that they can do stuff no other character can. And there are 30 of these unique characters.
On top of that, as others have mentioned, TRPG tend to be more linear/less procedural/sandboxy, but there’s a good tradition of sandboxy TRPG, so I don’t see that as strong of a distinction.