Aperture increases flash's range of coverage?

A beginner strobist is here.

Is it true that I can effectively increase flash's range by increasing an aperture?

Can I instead bump up flash's power (EV) to the same effect?

Also, this is really confusing to me: when I'm decreasing a flash output right from my D7000 - my SB800 info screen shows increase in range distance. Isn't it supposed to decrease the range distance?

How does changing flash output from a camera differ from changing EV value on the flash itself?

Brrrrrr........