The difference IMO is texturizing is using a mild relaxer that was never meant to fully straighten hair to change the texture of your hair by loosening your coils slightly, while texlaxing is using a relaxer that is meant to straighten hair fully but applying for less time that directions say so you only slightly loosen your coils. So you may get the same results from both processes or you may get less loosening or more loosening with texlaxing than texturizing, depending on how long you leave relaxer on.
So I don't think you can really know if one's "safer" than the other unless you knew at what point you'd have to wash off the relaxer during texlaxing so you don't break bonds to the point a texturizer would. So as far as using color, I don't know if one's safer than the other.
If I were the one doing it, I'd go with texturizing because the amount of time to leave the product on would not be up to me to decide but I could just follow the product's directions and get the results I wanted. I'm not very comfortable with the guesswork that I feel would be required of me in texlaxing.