Yes, you are wrong.
Lower power, cheap ammo is marketed as target and training ammo for those who want to shoot cheaply hence ammo makers market it as such. Yeah you can train with weaker, low power target ammo but if it isn't what your weapon you intend to defend you aren't doing yourself any favors. If you shoot enough you can definitely tell the difference between between weaker loads and self defense loads. If you can't tell the difference, then you don't shoot enough.
That said if you want to use target ammo for a class because it helps keep your training costs cheap, I won't judge; but if you intend to constantly train with target ammo and swap in the high powered load when you get home without ever shooting it, then I will.