Which one of them is the time-reversed wave-function, $psi^{ast }left( x,tright) $ or $psi^{ast}left( x,-tright) $?

If the wave function $psileft( x,tright) $ is a solution of the spinless
time-independent Schr$ddot{mathrm{o}}$dinger equation,
$$
ihbarfrac{partial}{partial t}psileft( x,tright) =left[ -frac
{hbar^{2}}{2m}nabla^{2}+Vleft( mathbf{r}right) right] psileft(
x,tright)
$$
then, $psi^{ast}left( x,-tright) $ is also the solution
$$
ihbarfrac{partial}{partial t}psi^{ast}left( x,-tright) =left[
-frac{hbar^{2}}{2m}nabla^{2}+Vleft( mathbf{r}right) right]
psi^{ast}left( x,-tright)
$$
and can be defined as the time reversed wave function of $psileft(
x,tright) $

$$
psi_{r}left( x,tright) =psi^{ast}left( x,-tright)
$$

However, in many discussions about the time-reversed operation, the time
reversed wave function $psi_{r}left( x,tright) $ is obtained by applying
the time reversal operator $K$, which is the complex conjugate of the wave function,

$$
psi_{r}left( x,tright) =Kpsileft( x,tright) =psi^{ast}left(
x,tright)
$$

So my question is, which one is the time reversed wave function $psi^{ast
}left( x,tright) $ or $psi^{ast}left( x,-tright) ?$

The general expression for the time-reversal operator $T=UK$ (Eq. (4.4.14) in
Modern Quantum Mechanics by J. J. Sakurai), where $U$ is a unitary operator
and $K$ is the complex conjugation operator. For spinless case, one can choose
$U=1$, so $T=K$.