A serialized television series contains a congruent storyline across the season with one episode connecting to the next. You cannot just turn on to a random episode and get the storyline, you need to watch everything that came before. Think Gotham or Superman and Lois for DC examples. Non-DC examples include Game of Thrones, Breaking Bad, True Detective, Stranger Things, etc.
An episodic television series contains anthology episodes that are generally unconnected to one another across episodes. You can turn on a random episode and get a fully contained story from start to finish without missing any prior knowledge. A good example of a DC show in this format is Batman: The Animated Series. Outside of DC, good examples include Star Trek, Law and Order, Black Mirror, and pretty much any sitcom.
Then there's the weird "blend". This is where it tries to have the best of both worlds. Sometimes it works. Sometimes it doesn't. For the most part, episodes are episodic and self-contained, but in the background, there is some overarching story that can only be picked up by watching all of the episodes that contribute to that story. This has become more common in modern times. Most of the CW Arrowverse shows did this, having "villain of the week" formats for the beginning of the seasons, with a background story that built up and was concluded in the last few episodes. This is also similarly done in shows like My Adventures with Superman, Smallville, Supernatural, X-Files, Buffy the Vampire Slayer. Batman 1966 also did it's own type of "blend" in the first two seasons, with the ending of an episode involving Batman and Robin falling in a trap and getting out of it at the start of the next episode, however that was the only continuity and for the most part it was purely episodic.
So which of these would work best for a live action Batman and Robin show set during Dick Grayson's tenure as Robin. There aren't that many iconic storylines from Dick's tenure since it was the silver age, so both formats could work. I would lean towards serialized if the show was featuring Tim, considering at that point, the comics were telling long stories that blended into one another. But what do you think would work best? I'd prefer choosing either fully episodic or fully serialized. The current way shows "blend" the two makes a show seem low-quality and tacky to me with the same formulaic "monster/freak/meta of the week" format happening every episode and then some bigger threat in the background. But if you can come up with a better "blend", I'm all ears.