What would irreducible character mean if the characteristic of a field is not zero?

Question

Let $G$ be a finite group and $F$ be an algebraically closed field such that $char(F)$ does not divide $|G|$.

Let $\chi_1,\chi_2$ be the characters corresponding to representations $(\rho_1,V_1),(\rho_2,V_2)$ respectively.

If $\chi_1=\chi_2$, then are $(\rho_1,V_1)$ and $(\rho_2,V_2)$ isomorphic?

(I only know that this is true when the given field $F$ has characteristic $0$, (not necessarily algebraically closed.))

This must not be true, because if $L$ is a simple $F[G]$ module and $char(F)\neq 0$, then two $F[G]$ modules $M=L, N=L\oplus\cdots\oplus L$($1 + char(F)$ times) have the same character, but are not isomorphic as $F[G]$-modules.

So there are two possible definitions for irreducible characters:

1. A character is irreducible if it is the character of some simple $F[G]$-module.

2. A character is irreducible if it is not a pointwise sum of two nonzero characters.

These two are obviously equivalent when $char(F)=0$, but I'm not sure whether these are equivalent when $F$ is algebraically closed and $|G|$ is not divisible by $char(F)$.