In what ways are the individual Persona games connected?

I have only played Persona 5, and it has encouraged me to pick up the other games in the series. I know that they're all stand-alone, but I'm curious:

In what ways are the games related?

Are they comparable to the Final Fantasy games, where only things like enemy and spell names are connected, or is there a bigger tonal/plot/other link between the games? I don't mind minor spoilers if they help answer the question.

There are references to other Persona games scattered throughout the series, but their plots are mostly contained. Having only played the most recent 3, I can only speak for them. However, here are some examples:

In Persona 3, the online game you play for the Hermit arcana is called "Innocent Sin Online" -- a direct reference to Persona 2: Innocent Sin.

In Persona 4, you make a field trip to Gekkoukan High, which is the setting of Persona 3. You even meet some of the characters, though much of the main cast has since graduated or is not present.

Persona 3 and 4 are closely tied due to the time they take place and there are quite a few crossovers, most if not all being canon.

In Persona 5, there are references to Rise Kujikawa and her pop idol career as well as references to the "boy detective" Naoto Shirogane.

Another fun one is that Vincent Brooks made an appearance in Persona 3 Portable at one point as a means of building hype for the release of Catherine (a different ATLUS title, apart from the SMT or Persona series).