Mandalorians have been divided into factions, and as of Boba Fett's armor. Since then, Mandalorians have been a fascination among fans.
The Expanded Universe elaborated on George Lucas' basic setup for the Mandalorians and sought to build a culture that could rival the Jedi and Sith without relying on the Force. Perhaps the best of those stories were told in the Knights of the Old Republic video games and comics, but unfortunately, due to Disney's relaunch of Star Wars canon, all of those tales have been disregarded. Some have found their way back into canon through the Star Wars Rebels, and of course, The Mandalorian, but most of them can't work anymore.
Slowly but surely, though, The Mandalorian has been revealing bits and pieces of Mandalorian culture and what happened to them during the Galactic Civil War. In The Mandalorian series premiere, it was revealed there was a Great Purge; the Empire killed most of the Mandalorians and stripped Mandalore of its beskar steel. Years later, Bo-Katan Kryze and her Nite Owls are taking the fight to the Empire and aim to reclaim their home world. But through her introduction, it appears the Mandalorians aren't as united as they once seemed.
Din Djarin & The Tribe
Like Baby Yoda, Din Djarin was once a foundling. His planet was terrorized by the Separatists during the Clone Wars and his parents were killed by the droid army. But luckily, Din Djarin was saved at the last minute by Death Watch - a group of Mandalorians who opposed the pacifist New Mandalorians government led by Satine Kryze - and he was raised to be a Mandalorian. At some point following the Republic's fall and the Empire's rise, the Mandalorians were killed by the Imperials during the Great Purge, which is presumably when they lost control of the planet Mandalore. What happened immediately after that is unknown, but by the time The Mandalorian takes place, many Mandalorians were in hiding.
Din Djarin became part of the Tribe, a faction that adhered to the Mandalorians' antiquated, warrior past; for the most part, they lived underground on the planet Nevarro and would only leave the covert one at a time, fearing they would expose the Tribe. (Eventually they did; several Mandalorians were killed on Nevarro before the covert moved elsewhere.) Furthermore, the Tribe believed in the Way of the Mandalore, which included never removing their helmets in front of another living being. And based on what Bo-Katan Kryze told Mando, the Tribe appeared to follow the ways of the Children of the Watch - a group that separated from other Mandalorians - which is presumably either the evolution or splinter group of Death Watch.
Bo-Katan & The Nite Owls
For thousands of years, Mandalorians were seen as the most formidable warriors in the galaxy, so much so that even the Empire initially resisted fighting them. But during the Clone Wars, the Duchess of Mandalore, Satine Kryze, sought to bring about a new era, one rooted in peace instead of war. It was an unpopular decision among some Mandalorians, notably Death Watch, which Bo-Katan Kryze (Satine's sister) was a member of. Bo-Katan fought alongside Death Watch's leader, Pre Vizsla, and later, Maul and his Shadow Collective. Together they reclaimed Mandalore from the New Mandalorians, but rather than have Pre Vizsla lead the Mandalorians as the new Mandalore, Maul took control of the world, killed Pre Vizsla in a duel, and executed Satine.
Bo-Katan believed in restoring the old ways, but only to an extent; she told Maul that Mandalorians would never accept an outsider on the throne. So she and her Nite Owls - a group of elite female Mandalorians, identified by their blue Mandalorian armor and owl-designed helmets - broke off from Death Watch and temporarily ed forces with Ahsoka Tano and the Republic's 501st Legion to defeat Maul and take back her home during the Siege of Mandalore. Since then, Bo-Katan and her Nite Owls have fought against the Empire (as seen in Star Wars Rebels and The Mandalorian) and have tried, once again, to save the planet Mandalore. In the years since the Clone Wars, Bo-Katan has come to regret her involvement with Death Watch, but she and the Nite Owls have always remained true to their cause; now it's just not in opposition to other Mandalorians.
Boba Fett (& Other Fake Mandalorians)
Bo-Katan Kryze and her Nite Owls are Mandalorians just like Din Djarin and the of the Tribe, even though the latter group had split from Mandalorian society to follow an ancient way. Then there's Boba Fett and his father, Jango Fett, who actually aren't Mandalorians at all. Despite the fact that Boba Fett is the character that inspired the Mandalorian race in Star Wars, he has never been a Mandalorian, but is instead a clone who wore Mandalorian armor, just like Cobb Vanth aka the Marshal did in The Mandalorian season 2, episode 1.
As revealed in Star Wars: Episode II - Attack of the Clones, Jango Fett was a bounty hunter whose DNA was used as a template for the Republic's clone army. All he wanted as payment was an unmodified clone for himself - Boba Fett. It was then explained by Prime Minister Almec in Clone Wars that, in spite of wearing Mandalorian armor, Jango Fett wasn't a Mandalorian; he somehow found that armor and wore it around. Still, that didn't mean Boba Fett couldn't become a Mandalorian himself. However, instead of dedicating himself to the Mandalorian creed, Boba Fett became nothing more than a common bounty hunter.
What's unique about the Mandalorians is that technically anyone can become one. No one needs to be born on Mandalore or be born into a prominent Mandalorian family; they can come from any planet, race, culture, or religion. All they have to do is train and dedicate themselves to the creed. Boba Fett chose not to follow that code of honor and instead become an outlaw, which means he's not a Mandalorian, just like his father. Unfortunately it's easy to wear Mandalorian armor and off as one, but it's not easy to actually be one.