Asking a layman about a knight, they would probably respond with a description of a nobleman on horseback, wearing heavy armor and charging into battle. The origins of this trope are, as always, more intricate than the stories we share. While the popular mythology of knights is based around King Arthur and other such tales, the knight is much more complex than a chivalric paragon.
The word “knight” is derived from the Old English Cniht and the West German Kneht and drew inspiration from the Roman Equites, a term referring to armored, mounted soldiers. Originally, the term we know as knight simply referred to a retainer of a noble, and by the Middle Ages became a term for someone in the service of a king. By the time of the Hundred Years War, the knight had been solidified as a noble who went into battle on horseback wearing heavy armor.
However, this definition is not the only version of a knight we know in the modern trope. In the late Roman and Byzantine Empire, the equivalent of the knight on the battlefield was the Kataphraktoi, literally meaning armored in Greek. These warriors were professional soldiers and did not have the same noble titles as their western counterparts. Due to Byzantine influence in the Arabian peninsula and North Africa, the style of Kataphraktoi was adopted by Turk, Egyptian, and Berber nobles as well. The last knight-adjacent figure in pop culture is the samurai. On the surface, there are many similarities like the heavy armor, noble titles, and code of honor, to name a few. The samurai functioned closer to the original meaning of knight, working as retainers for nobles rather than ruling as the nobles themselves. And while samurai did fight mounted, they dismounted in combat more often than European knights.
So when designing a ttrpg or fantasy world, keep in mind that not every fighter wearing heavy armor on a horse is a knight. Even if they follow a code similar to the chivalric code of a knight, they may not have formally been granted the title. I personally am a fan of including Kataphraktoi as retainers for nobles in my setting, mostly because of the aesthetic. I would love to hear some of your replacements or alternates in the comments and feel free to share any questions or concerns as well.