Is it normal to want to be underweight but not anorexic?

Anorexia isn't defined by how thin someone is. It's an eating disorder. Someone could be dangerously skinny and not anorexic. Just the same, someone could be at an average weight and be anorexic.

Regardless, you shouldn't be aiming to be anything but what's healthy for YOU. There's no way you can be underweight and at a healthy weight, just like you can't be overweight and at a healthy weight. It's contradictory. Look at your BMI. As long as you stay in a healthy zone (specific to your height and body build), you should be alright.

Take it from someone who has both had annotexia and spent many years their life being underweight (Heck! I might still be considered underweight!) - its not always a pleasant experience just being underweight. Even if you eat healthy, If you're underweight you'll be bound to experience some form of negative health impacts. While some parts of society may still see an appeal in being underweight, I no longer can. I used to look very bizarre, to put it lightly. Then, downright ghoulish and of the living dead. I don't like the feeling of being chronically weakend and easily toppled over from a gust of wind. We both have very different ideals, which is fine so long as you don't end up developing anorexia. I just can't for the life of me wrap my head around the appeal you find in this. Be safe.