Sir, I will attempt to describe the kicks/names used in MDK and WT/Kukkiwon. As you have mentioned there are variations in about every derivative of TKD. I think the common denominator here is that we/other styles train the kick as a defensive tool but do not give it a separate, specific name. The mechanics are only slightly different whereas the defensive kick is typically and low to mid level kick, whether delivered from the inside or outside. Opportunity recognition is stressed. Simply meaning 'what targets are available and most opportunistic'. The "Footsword" is what we describe as the "blade" of the foot. This would b an Outside crescent kick. Starting travel is from inside the body, continuing the motion traveling to the outside of the body. "Reverse Footsword" is what we describe as the 'ball' or simply inside of the foot. This would be an Inside crescent kick. Starting travel is from outside the body with the motion ending inside the body. I suspect the "Downward Kick" is the easiest to disseminate, especially with your "Pick Axe" description. We commonly call this just an Axe kick. This kick has the same motion variants; inside, outside, and straight. Not as common but there are variants for front leg or rear leg for any of the kicks. More of the "any port in a storm" category but good to have the elasticity in the mind when needed. I Always appreciate conversing with you Sir.