Sure, different uses but not drastical ones. That`s a conversation that applies more on execution, over anything else. Tynion and the others (whether you enjoy them much or otherwise) did not change the core of the character nor his morals, nor much of his voice in order to push or make a voice that wasn`t there. In very RPG terms, Jason`s personality/stats remain consistant across the board, with some writers tackling it in interesting ways and a few failing to do the same in major crossovers (which it`s is own animal in terms of format - even after all this time I still see Wonder Woman fans claim that COTIE to be a disservice of the character`s use and role).
Exemplary wise, Tynion, Greg Pak, Tomasi and Loedbell used the same character but a few may have tackled it differently.