Not sure if this is covered in the Diskwars FAQ, but from the X-Wing FAQ
“At” vs. “Within” “At” means the closest part of the target’s base touches that range section. For example, when attacking a ship whose base touches both Range 2 and Range 3, that ship is at Range 2. “Within” means wholly within. For example, normal tournament deployment is “within Range 1 of the table edge.”
I think it's safe to assume the same verbiage applies.
"When a ranged attack or ability specifies a range, the player must measure the range using the range ruler. To do so, players measure from the surface of the disk that is using its ranged attack or ability to the surface of the other disk. The point where the range ruler touches the other disk defines the measured range between the disks. If the measured range is within the maximum range of the disk using its ranged attack or ability, the other disk is in range."
It is implied that "completely within" means that all the disk must be within the range, not just part of it. The only specification in the rulebook for "completely within" is the deployment rules on page 5. It's not exactly the same thing but it's pretty reasonable to assume this interpretation is correct.
So what in X-Wing is "at X range" in WHD becomes "within X range", while "within X range" in X-Wings becomes "completely within X range" in WHD.