Say 2 tires both same brand and all, just different sizes

205\60\15
175\60\15

I always thought is was tire width, but a friend is telling me it's not.

are the numbers like this?
width\side wall height\rim diameter

here's the reason I'm asking here. I want to auto-x and my current tires are 175\60\13 I would like to find some better tires.

thanks