Jax?

No Jax is not garen.

Jax is more mobile and more late-game oriented.

theyre both bruisers, but they play as different as they can.

jax is really mobile lategame with a less than 5 second cooldown on leap strike. hes also an on hit carry who works entirely with auto attacks and auto attack resets.

garen is much slower and almost entirely a caster.

Nope, Jax has a stun, benefits from attack speed(thus Trinity Force got even better for him), cannot be damaged by autos during certain frames, oh and he heals for more damage than he receives in most occasions late game. If the healing is what you're referring to, then no, Garen heals out of combat, Jax heals per auto from items like hextech gunblade and bork.

tbh they are the same, they both press E to spin and Q to jump onto people