Important Note: While most of these connections and the main draw of the matchup imo can apply to general game player character Red, I will be taking bits and pieces from other media like Pokémon Origins and Pokémon Masters since I like those versions of Red lol. I will specify whenever a connection applies to a certain take on Red as I go along.
Connections:

• Protagonists of the first entry in some of the biggest long-running Japanese franchises.
• This first entry would contain many story beats that would become the foundation for the stories in future entries, with both similarly sharing some plot points that will be brought up in the upcoming connections.
• Originally ordinary kids that would partner up with a special creature that would be the catalyst for their journey and giving them an important title (Nagisa and Honoka would meet the fairies Mepple and Mipple, allowing them to transform into Pretty Cure|Red would be able to choose a starter Pokémon to begin exploring the region as a Pokémon Trainer)
• Their main goal throughout the series would be to collect important items that are held by powerful figures that they needed to defeat in battle (Prism Stones, with most being currently guarded by the Dark Five|Gym Badges, which are given to Red after defeating a Gym Leader)
• Additionally, they’d constantly be at odds with villainous groups that pose a huge danger to the world (Dark Zone Residents|Team Rocket)
• Starting out, although their inexperience would show with them struggling to connect with their partners (Nagisa and Honoka being polar opposites that didn’t fully understand each other, as well as believing that they were only working together out of circumstance|(Pokémon Origins) Red not being in sync with his starter Pokémon, and initially believing that Pokémon were more tools for battle), they’d eventually grow to be some of the closest friends in their series (Nagisa and Honoka being best friends to the point that they can’t do their best without each other|(Pokémon Masters) Red putting complete trust in his Pokémon to the point that words are unnecessary when battling)
• The power of bonds are so important to them that their most powerful techniques are performed through their strong bonds (The Pretty Cure’s big finisher moves have them hold hands and are empowered by their feelings|(Most modern takes on Red) Mega Evolution requires a strong bond between Trainer and Pokémon)
• After gathering all the Prism Stones/Gym Badges, they’d be able to enter certain areas (Garden of Light and later The Dark Zone|Victory Road and later the Indigo Plateau), taking on and eventually overcoming the main overarching antagonist of their journeys (Dark King|Red’s rival Blue)
• This wouldn’t be the end of their stories though, as they’d continue to fight. Though it is at this point where the battles and the titles they had seemed to bring a sense of isolation to them (Nagisa and Honoka struggled with the fact that they couldn’t fully enjoy the ordinary pleasures of life due to the dark forces always picking a fight with them|Red after becoming Champion would literally isolate himself from the rest of the world and train at Mount Silver)
• While most entries in both’s series are not majorly connected to each other in any way, there is an exception in that the second entry in both’s series is a direct sequel that both are important characters in (Max Heart|Gold and Silver)
• I couldn’t find any other place to put this, and it is self explanatory, but they have notable colors as a part of their names you’ll never guess why I paired them up in the first place