Ringing metal on metal, long duels with elegant, acrobatic moves and with very light clothing are the realm of sword and rapier combat as seen in shows like Xena and Zorro. A rather amusing display if one has ever wielded such a weapon for real. Swords are weapons designed for killing and armor is meant to prevent injuries.
Combat with the sword, also called "Heavy combat" assumes that the goal of a fight is to "kill" your opponent, without getting killed yourself in the process. In terms of our style of combat this means that one should fight fairly, in a manner befitting a knight and always with full contact (this means you really try to hit your opponent and don't just smack the weapons against each other). However, since nobody intends to truly injury the opponent or get injured themselves, safety regulations have been implemented that prevent basically all injuries worse than a few bruises:
For one thing, real steel weapons where exchanged for rattan weapons that have been saftey taped. They are very similar to real weapons in both weight and handling and they do not splinter upon breaking as a bamboo or wooden weapon would. Historically speaking, wooden swords were used already during the middle ages. For one thing it was too expensive to damage to a good sword by notching it through contact with another weapon and due to the level of medical care at the time serious injuries could easily lead to amputaton or even death.
Beyond that we use a minimum set of armor that must be worn during combat. This includes a helm, body protection, joint protection, especially for the hands and extra protection for sensitive areas such as neck, kidneys and groin. In addition you need to wear sturdy shoes. All of this can look very different from one person to the next, because many fighters build and care for their own armor. All equipment is tested for safety hazards prior to combat. We have one basic rule: Safety first!
In order to participate in a tournament a fighter must be authorised, which means he must have displayed before a marshal (a type of umpire), that he knows how to wield a weapon safely, fight fairly and keep a clear and level head. In a tournament there is always one marshal on the field to step in should a dangerous situation (loose armor, kids/dogs running onto the field, broken weapons etc.) arise.
The rules are based on damages a real weapon might have caused. This means one tries to hit lethal areas of the body with some force. Legal target zones are the entire body from the knees upward. Hits which would have penetrated armor in a real fight count and lead to the loss of the hit body part (i.e. arm --> the hit arm is held behind the body; leg --> the hit fighter continues fighting on his knees). Since nobody can really determine how well a strike actually hit, it is absolutely important that the hit person is fair and acknowledges a good hit.
Forms of sword combat are combat with the spear, the mace, a two handed sword or with two swords, to name a few.
The basic concepts of fencing are the same as in sword combat. Behaving in a knightly manner, fairness and safety. Usually fencing is done with regular epee or rapier.
Even though it might be less obvious, here too we wear protective gear. Fencing mask, gloves, sturdy shoes, very robust fabric covering the upper body (four layers on head and torso) and solid groin protection are required.
Here too the fighter must be authorized in order to participate in tournaments and of course there is a fencing marshal present during the tournament.
Since fencing came into fashion during the renaissance, the fencing rules assume that the opponents wear regular clothing (doublet, shirt, sturdy pants). That is also why every hit that is more than a scratch is considered to be a serious injury. A stabbing hit counts as soon as the blade begins to bend a little, a cut with tip or edge of the blade must move across the body for 20 cm in order to count. Glancing strokes do not count and actual hits are not permitted. Here to the hit fighter must call the blow.
Forms of fencing are combat with two rapiers, rapier and dagger, rapier and sheath, rapier and coat, just to name a few.
For those who think that rapier or epee are not close enough to the historical weapons may use rapiers of historically accurate weight and Schläger blades. These weapons however require skill with a rapier and extra protection.