I’ve taken H2H, rapier, short sword and shield, sword and dagger and a few other stage combat classes in both UK and US — and then in production you usually just get “any old sword” (usually a heavy one, as Tybalt in R&J they gave me this really fancy grip with a finger hole for my index, but it made supranative positions difficult)
You’re right in that they are based on real combat — you learn fencing footwork and guards, but also you’re learning a mix of slight of hand (how to “knap” - fake the sound of hitting /being hit while reacting like its real), and safety instructions. As someone who came from ballroom to jazz/modern dance to acting, it’s more like dance, especially freeform contact improv dance, than it is like actual fighting.
I imagine in real fights-to-the-death there’s a lot less concern about safety, distancing and the lines your body draws in movement, and more about hurting the other fellow as efficiently as possible.