Jewry is not monolithic and much of ones religious/spiritual/social status are the result of "accidents" of birth.
Among such divides is the one that separates the כהנים בני אהרן =Aaronic Priests from the balance of their לויים =Levite brethren. We know that in fulsome Judaism these two distinct categories of Jews have diverse duties in the Miqdash, that only the Kohanic duties requires service in uniform, that the Levites status was initiated through whole-body shaving and תנופה = lifting/waving while that of the Kohanim was initiated through anointing and that the two groups, both of whom received no homesteads in the Land of Israel, receive different types of stipends/ material support from the other tribes of Israel. In contemporary Judaism the only perceivable differences are the sequence of aliyas at Torah Reading and that , prior to the Priestley blessings the Levi'im are the hand washers while the Kohanim are the hand-washed .
The question is what is the underlying difference between the two? The answer may be alluded to by the Zoharic passage that says לוי-טהור....כהן-קדוש = Levi-Tahor, Kohen-Qadosh (don't have a cow...I first saw it in a secondary source and googled to get the link). The Aaronic priests are associated with sanctity/qedusha while the Levites are identified with purity.
The concepts of purity and sanctity are related but are NOT synonymous. It is possible for something to be pure without being sanctified but sanctity abhors impurity. The impure through contact with the dead were prohibited from accessing the Temple Mount. Many types of impurity invalidated the Avodah=Temple service of a Kohen. A Kohen is prohibited from impurity through contact with the dead. Sanctified offerings are invalidated from being sacrificed on the altar if they become impure and sanctified edibles , even קדשי גבולין such as Terumah, must be burned if they become impure. (Parenthetically, per the Maharal, this is explanation for why an adulterous bas Kohen is executed through internal burning rather than through strangulation like her paramour. One of the Torah's "logical inconsistencies" that I explicated in this post yesterday. It's not that she is being punished more severely. It's that her's was a Miqdash level sanctity that became impure through adultery and must therefor be "disposed of" through burning.)
The only takeaway that I can thresh out of all this is that just as one MUST be a Levi in order to be a Kohen (the reverse is not true) things must be pure in order to be sanctified but need not be sanctified in order to be pure.
Something to ponder on Chanuka is that although we emphasize the Kehuna of the Khashmonaim who wrought the Chanuka miracles, the miracle itself was effected through a flask of pure oil not merely sanctified oil. The liturgy of Ahl HaNisim= "for the miracles" that states = "you handed over the impure (Greeks) to the pure (Maccabees)" seems to be emphasizing their Levite identity rather than their Kohanic identity. In light of the Zohar quoted above this seems odd.
IMO Persian (AKA Iranian Jews) possess the loveliest Jewish surnames of any עדה . I personally know some who's surnames are לוי-טהור and כהן-קדוש