Fyraltari watches The Clone Wars (2008) for the first time

[Jasdoif]

I'm sure this has been changed numerous times, but I have the impression that successfully mentoring a padawan to Knight-hood is a sign of being eligible/worthy of the title of Jedi Master.

Thinking about that again, that doesn’t mesh with Obi-Wan being a master when Anakin is still a Palawan back in Attack of the Clones

Okay, I dug around...and while successfully training Padawans (or depending on where you look, a Padawan) is the most common, one can also attain the title of Master by completing a modified version of the Trials of Knighthood, or being recognized by the High Council for service to the Republic.

Of course, if anything of the sort had been intended from the beginning, those trials would have their own fancy title (like Trials of Mastery) like most things in Star Wars; so this sounds like an official excuse for the discrepancy you noted, and the "service to the Republic" bit is probably supposed to justify Anakin's expectation of being made a Master on his appointment to the High Council.