The thing about martial arts is that they work: if you do them properly, you're going to kill someone (or be killed). Every group that does stuff with swords, therefore, has to sacrifice something to ensure that everyone can have fun again next week.
In HEMA, it's the aesthetic that's sacrificed: we (I'm one of them) wear gear that makes us look like modern riot police, but the weapons are (at the very least) historically weighted, and the techniques are from historical fencing manuals. There's a lot of arguing over the interpretation of medieval manuscripts in the community.
Re-enactment groups wear historical clothing, so they have to reduce the scope of their combat: they typically disallow strikes to the head, for example.
The Society for Creative Anachronism dispense with everything but the aesthetic of history, and consequently have the most fun.
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