"Magician" (マジシャン Majishan) is an archetype of cards solely supported by the manga effect of "Magician's Circle" and "Magicians Unite". "Magicians" don't have a specific focus nor do they have any relations.
"Performapal Pendulum Sorcerer" is a "Magician" card because it has 「マジシャン」 in its Japanese name.
During the original Duel Monsters, "Magician" cards were part of the class known as Magic User. Each Magic User has a particular Alignment: Black Magic, White Magic, Demon Magic or Illusion Magic. The different types of Magic User have strengths and weaknesses depending on which type of Magic User they are battling.
The most notable Magic User was the "Dark Magician", as many cards that were used on "Dark Magician" in the manga and anime, have the kanji 「魔術師」, 「黒魔術師」 or 「黒魔族」 in the card text. Cards like "Magical Hats", "Magic Cylinder", "Magic Formula" and "Magical Dimension" have the kanji 「魔術師」 "Magician". Cards like "Mystic Box", "Nightmare's Chains" and "Dark Magic Curtain" have the kanji 「黒魔術師」 "Dark Magician". Lastly, cards like "Dark Renewal" and "Thousand Knives" have the kanji 「黒魔族」 "Black Magic User". The "Dark Magician" was used by Yugi Mutou, Dark Yugi and Pandora.
During Dawn of the Duel arc in the Yu-Gi-Oh! manga, Yugi Mutou's "Silent Magician" was introduced. The "Silent Magician" is different from the "Dark Magician", as it doesn't have a stated Alignment nor use any Magic User support cards. Instead, "Silent Magician" relies on its effect to increase its own LV and ATK each time the opponent draws a card.