Because as a lifelong fan of both, I've noticed a ton of them:
The Special Weapon (Lightsaber and Wand): A weapon where each example is unique to the wielder, and is powered by something special in the center of it (crystal for a lightsaber, core for a wand).
The Main Hero (Luke Skywalker and Harry Potter): Orphan raised by his aunt and uncle (the latter of whom doesn't want him to embrace his special powers and be a hero), is learning to use his special powers and a magic weapon, and is very angsty and unlucky in love before eventually settling down with a badass redhead and getting sons named after dead mentors. Both are also (falsely), rumored to have originally been female/fused with their main female friend.
The Main Male Friend (Han Solo and Ron Weasley): Unconventional, reckless, and anti-authority but ultimately also very reliable, courageous, and loyal. Falls in love with the hero's main female friend after a period of bickering, sniping, and sexual tension.
The Main Female Friend (Princess Leia and Hermione Granger): Pretty brunette who is the one that all the female fans look up to as an icon and all the male fans have a crush on. Intelligent, helpful, badass, reliable, and with a sharp wit. Falls in love with the hero's main male friend after a period of bickering, sniping, and sexual tension. Alternates between advising, empathizing, and scolding. Finally, both are popularly rumored to have originally been the main hero/fused with the main male hero (and in both cases it's a myth).
The Kind Mentor (Obi-Wan Kenobi and Albus Dumbledore): Wise, bearded, elderly teacher of great power with a gentle and warm sense of humor who serves as a paternal substitute for the orphaned hero, and who is killed by the secondary villain. Also friend/former friend of the secondary villain.
The Redheaded Girlfriend (Mara Jade and Ginny Weasley): Caustic-tongued, badass redhead who is initially manipulated by the main villain before falling in love with and marrying the main hero. Has a son with the main hero named after one of the hero's dead mentors.
The Sympathetic Secondary Villain (Darth Vader and Severus Snape): Tragic, misanthropic villain with a very dry sense of humor garbed in all black with a cape who kills the hero's kind, elderly mentor in front of him, is remorseful and self-loathing, and was in love with the hero's mother before becoming evil (including from a very young age). Both also had unhappy childhoods and die redeeming themselves.
The Pure Evil Primary Villain (Darth Sidious and Voldemort): Multi-named, sadistic, egotistical, sociopathic arch-villain who desires immortality, is immensely powerful, looks down on those who don't have the mythos' special powers, is a tyrannical dictator, and is pale, deformed, and garbed in simple black robes with a hood. Both are also completely failure-intolerant, killed their own fathers, manipulated the hero's redheaded girlfriend for a time, came back from the dead repeatedly, and are technically responsible for the death of the hero's parents (albeit indirectly in Palpatine's case).
The forbidden power source (Dark Side of the Force and Dark Magic): Dark variant of the greater special powers in the mythos that let you do lots of cool but also destructive and harmful stuff. Not inherently evil, but favored by villains and so discouraged by non-evil characters. Each one has specific powers (such as Force Choke, Force Lightning, Force Drain, the Unforgivable Curses, etc.)
The evil, dark fascist organizations (Empire/Sith and Death Eaters): Mostly black clad bad guys who are blatantly evil, sadistic, treacherous, manipulative, and power hungry. Both are also blatantly fascist in their worldview and tend to look down on and persecute certain groups (including those who lack the mythos' special powers). Both have also regularly been likened to the Nazis/Third Reich.
The fangirled/fanboyed villain (Kylo Ren and Draco Malfoy): Angsty and petulant villain who is widely adored by the fandom despite their many awful qualities and neither one being all that sympathetic until later in their series. Regularly shipped with franchise's resident British brunette heroine.
The major female villain (Captain Phasma and Bellatrix Lestrange): Pure evil female villain who supports a fascist/pseudo-Nazi organization of bad guys, is treacherous and cruel, and has abused/tormented one of the main heroes. Both have also murdered members of their own families and are failure intolerant.
The dead mother (Padme Amidala and Lily Evans-Potter): Kindhearted, sweet, selfless, and capable mother to the main hero. Died when the main hero was just an infant and their death was caused by the pure evil big bad (albeit indirectly in Palpatine's case). Both were also loved by one of the main villains before he became evil.
The small but powerful teacher (Yoda and Flitwick): Small in stature but big in power. Kind-hearted yet quirky teacher, and both also have Elf-like features. Each also defeats semi-major and powerful villains (Dooku and Dolohov)
The female fan-favorite (Aayla Secura and Nymphadora Tonks): Colorful, female heroine who is a more minor but still beloved character by the franchise. Both are considered fan-servicey at least a little bit, and both are tragically killed in the last installment in their series.
The badass black guy (Mace Windu and Kingsley Shacklebolt): One of the only black people of note in their respective series. Big, bald, and incredibly powerful and committed to the cause and being a benevolent authority figure. Both also like purple.
The Bureaucracy (Galactic Republic and British Ministry of Magic): The main governing bodies in the setting; usually well-meaning but filled with corruption and/or incompetence. Eventually taken over by the main villain and reshaped into a fascist organization before then being reformed a second time to be better than the original after the main villain is deposed.
The School for Powered People (Jedi Temple and Hogwarts): Schools/academies where those who possess the special powers of their mythos go to learn about said powers and how to control them. Both are also places where the students live while undergoing their studies, and both buildings go up in smoke during the end of wars (Second Wizarding War and Clone Wars, namely)
The Hero's Father (Anakin Skywalker and James Potter): Powerful, talented, and well-meaning but also arrogant. Bears some physical resemblance to the main hero and dies protecting their son from the main villain, who is also responsible for their death.
The Hero's Uncle (Owen Lars and Vernon Dursley): Non-powered uncle who raises the hero after the death of his parents and also puts him to work from a young age. Does not want the hero to embrace his special powers, be special, or follow the path of his father.
The big hairy hero (Chewbacca and Rubeus Hagrid): Big, brown, and very hairy hero with immense strength and a heart of gold. Often supportive and sometimes uses a crossbow weapon (giant crossbow for Hagrid, and bowcaster for Chewbacca). Both are also members of often-persecuted species (giants/half-giants in Hagrid's case, and Wookies in Chewbacca's case).
The Dragon (Krayt Dragon and Hungarian Horntail): Self-explanatory
The Hero's Son (Ben Skywalker and Albus Potter): Insecure, youthful son of the hero and hero's redheaded lover who appears years after the events of the main story. Named after the hero's dead mentor and often feels pressured to live up to the awesome legacy of his father.
The Incompetent Villain (Greedo and Gilderoy Lockhart): OK, so admittedly this one is reaching a bit, but they ARE both inept villains who only really show up in one major installment each, their names start with a "G", and their downfalls come about as a result of a "mis-fire" while trying to take down the hero/heroes (in Greedo's case, not being able to shoot someone from across a table, and in Lockhart's case, a spell rebounding on him due to a faulty wand).
And to think people make fun of Lion King for supposedly being a Kimba rip-off...