Are you differentiating between a Thai style cut kick and a TKD style? Are you lumping both under roundhouse?
And obviously target selection is huge. Common peroneal thigh vs side of waist, for instance. Or brachial plexus.
Low TKD roundhouse kicks below the belt are usually feints with a switchover to strike high in the same action, they combine into a double kick.
I tend to put the Thai kicks in their own separate category from the general roundhouse because the hip movement (specifically turning over to go downwards instead of lateral, which makes sense given the stabilizing foot stays mostly pointed forward), rotation, foot placement, and points of contact are all different. The Thai cut kick has its own name, it’s separate from the roundhouse though they’re visually similar… I guess? The traditional roundhouse will have difficulty targeting the legs due it’s chamber, which is the Thai kicks’ specialty. I understand the confusion, the snap kick version of the TKD roundhouse that is mostly seen in sparring doesn’t move the front leg much but it also lacks turnover. You lift the knee in a front kick chamber and strike on an upward diagonal rather than horizontal. It’s a point sparring kick rather than a combat kick. Thai kicks can be used at much closer ranges with hip turnover, which you know.
Still, we’re getting into the variant ranges of kicks that are visually similar (I guess?) but very different in execution. There’s more than three different versions of the TKD roundhouse. The one I’m talking about is the roundhouse you see on television, the general roundhouse. This is the basic martial arts roundhouse with slight, minor variations between styles from TKD to Shotokan. It’s going to be the most recognizable to the widest audience.
The Thai kicks are unique, even in comparison to modern kickboxing with the way they move. The major difference between Muay Thai kicks and kicks from other martial styles is the range at which they function, which you know. Thai kicks work in the hand range versus the traditional kick range. Plus, the option to strike with the shin.
Krav Maga is the same way, it’s a different kick.
Muay Thai is a creature all it’s own, and deservedly so. In twenty years (or less) do its proliferation in the West and adoption in MMA/Hollywood, it’s going to have it’s own recognizable and famous version. That’s probably going to be one of the versions of the low kick that utilizes the shin.
Roundhouse tends be used as a catchall for lots of martial arts kicks, including kicks that have nothing to do with each other. I went with the generic. If I was doing the straight TKD kick, I’d mention the variety of different chambers for it depending on stance. I’m going with the one most people outside the martial arts community will be familiar with.
Call it the Chuck Norris roundhouse if it makes you feel better.