I can do a pretty good Axe kik but not as good as her's! Also her thiccness will add to the power.

E-er...you know what? I'm not correcting what the technicality is for this situation because I only know one version of an Axe kick..._{my words are vague when I say that...}

idk *shrug*
I know at least in taekwondo its just a straight up and then kick downward. Otherwise I wouldn't know what it'd be called from the air.

Hm...well you're not wrong, also it'd still be an axe kick! Kim Kaphwan does a stylish Axe Kick called "Kuchugetsuzan" which is an aerial version of "Hangetsuzan" which is basically a forward flipping axe kick that lands into a splits position. The aerial version is that but landing on your feet. So its still an Axe Kick, but I assume its super devastating as its a full body spin and twist that comes before the very fast and power kick straight downwards...er..well...technically speaking from more a standpoint that isn't from KOF XIII's damage amount for that attack.