It should be noted that most most modern Mandalorians don’t necessarily adhere to one of the following historical types. However, they’re cultural touchstones, points of contention and accusation. It wouldn’t be far wrong to say that these identities and their originators are used in discourse in the same way that various political agendas invoke founding fathers -- with a greater or lesser degree of accuracy. We’ve all witnessed the endless idiocy of ‘you’re no true Mando!’ -- ‘No, you!’ -- when in the end, virtually all Mandalorians fall somewhere between several of the listed stereotypes.
It's also worth noting that there is no one idea of what 'honor' actually means to a Mandalorian. Different eras had wildly different definitions, all of which have modern adherents. For example, for twenty thousand years or so, an 'honorable' Mandalorian was one who helped conquer and slaughter his neighbours, and remained loyal to his clan. As another example, Mandalorian mercenary work only began around 4,000BBY, and Mandos originally only chose mercenary work out of necessity, since they'd backed the wrong horse in a war or two.
The evolution and devolution of Mando principles can be dizzyingly complex, and even a basic summary is a serious task that would fail to do justice to the diversity involved. Some important stereotypes or archetypes:
MANDALORIAN CRUSADERS - The originals, ~24,000 to ~4,000 BBY. Conquer, oppress, expand. Zero internal command structure, zero internal division of labour, rule by the strong. Leadership was determined by single combat. Backed Qel-Droma, Keto, and then Kun during the big one, and got chopped down to size. Originally polytheistic, then sort of monotheistic (Kad Ha'rangir the war god), then worshipped war directly. During this period, the Mandos nailed down the Resol'nare, the Six Principles, which would define Mando civilization ever after. Armor was highly individualized.
MANDALORIAN NEO-CRUSADERS - 'We gotta get back to our roots,' ~4,000ish BBY. Conquer, oppress, expand, assimilate. These are the Mandos that Revan fought; he beat the crap out of them, to the point where the Clans split and scattered. (He'd later be partially responsible for their reunification via Canderous Ordo.) This is where 'anyone, of any species, can become a Mando' really kicked off, largely because of the heavy losses the Mandos took in the Sith Wars (and because the Resol'nare was silent on the subject). This is when armor got standardized, extremely so, and internal rank structures started existing.
In the aftermath of Revan shredding the Neo-Crusaders, this period is also when thug and merc work became a thing.
NEW MANDALORIANS - 'We're sorry,' ~740 BBY-20BBY. Pacifists. The Mandos got too big for their britches, and the Republic came in with what's called the Mandalorian Excision (a nice word for attempted genocide by orbital bombardment). The New Mandalorians were a movement that tossed aside the armor and the Resol'nare. They focused on technical skill and collaborative work, building huge arcology settlements in the blasted desert regions of Manda'yaim. Remind any Mando of the New Mandalorians sometime. I dare you. In case you were wondering, yes, this is where the 'you're no true Mando' debates really started. Thought they didn't peak until...
DEATH WATCH versus 'TRUE' MANDALORIANS - ~60BBY. The True Mandalorians followed the Resol'nare, plus the six hundred tenets of Jaster Mereel's Supercommando Codex - basically a big old volume of scripture. The Death Watch were a knee-jerk reaction to the True Mandalorians, and a throwback to the crusader days. Neither group had much use for the New Mandalorians, but it was the Death Watch who really hated them, and ultimately tore them down in 20 BBY.
It is very, very important to note that, depending on which Mando is saying that you're 'no true Mando,' they might or might not be referring to Mereel's True Mandalorian movement. They might just as well be referring to the Mandalorian Crusaders, in which case the True Mandalorian principles might well be the target of the 'no true Mando' accusation. You literally never know. It doesn't help that none of these five stereotypes could agree on what constituted honor, or whether mercenary work was acceptable or desirable. Personally, I feel that after the Clone Wars, all evolutions of Mando society, and internal debates about Mandoness, boil down to shifts between the stereotypes I just listed.
Today, there's no standardization, either inside the United Clans or inside the Mandalorian Empire. People who would have been considered Death Watch or Neo-Crusaders in previous eras commonly serve alongside people who would have followed Mereel. The label 'Death Watch' has been used by a few modern movements, but in reaction to wildly different things. Every Mandalorian runs around calling every other Mandalorian a fake, and every Mandalorian has Very Strong Opinions about what it means to be Mando. Those opinions might or might not line up with one or more of the historical stereotypes. I'm told that one Mandalorian Clan Chief recently fought a duel because the entire clan was called honorless based on principles that were current six thousand years ago, but haven't been since.
In the words of a wise man, the Mandalorians aren't an organization. They're a shared opinion with guns.