Is a brake flush the exact same thing as replacing the brake fluid?
Or is there a difference?
To replace it, you have to flush out the old brake fluid with new fluid.
See this answer on how to bleed brake lines for more details.
In some places, a brake flush might include some sort of additive used to clean the braking system. Its usually a gimmick.
Replacing the brake fluid itself is what it means. But flushes can vary between places and most of the time (from experience 99.999999999999%) its a gimmick to get your money.