Better Call Saul is a prequel spin-off of Breaking Bad so it’s basically setting up characters and plot points to where they were when introduced in BB, but also doing a lot of its own thing. It ostensibly follows Saul, the sleazy lawyer guy in BB, but it also devotes significant chunks of its runtime to other future BB characters (also, amusingly, you’re only sort of right about there being a guy named Saul since Saul is a pseudonym/stage name that isn’t really used until the most recent seasons of BCS)
So there’s basically 3-ish main plots going on that sometimes intersect, so they’re not like strictly separate:
The Jimmy/Saul lawyer plot, that sets up the BB character of Saul and how/why he does the things he does and knows the people he knows
The Mike plot, that sets up the BB character of Mike and why he’s involved with Madrigal/cartel stuff, how he knows people like Saul and Gus, and his mindset
The Salamanca/cartel/Gus plot that goes more into that rivalry and how the pieces are set up to fall as they do in BB
Oh yeah also each season starts with a little post-BB plotline thing.
idk it’s hard to explain why the show is so good because on paper it sounds kinda bland and when they first announced it I was like “a prequel about the sleazy lawyer guy from Breaking Bad? No thanks!” it’s slower paced than Breaking Bad, and you know where these characters (well, most of them, notably 2 BCS characters are not in BB so their fate is up in the air), which are all stuff that should make the show significantly less compelling but, idk, I’m hooked