In Anna Karenina, one of the characters is a Princess but rejects a servant calling her “your highness” because, she says, she is not royal
How can a princess not be royal?
I’m pretty sure the spouse of a prince is not considered royal. And a “princess” can also be the daughter of a non-royal noble.
In Tsarist Russia, Princess kiss you!
Sorry. Really, the term “Prince” or “Princess” is a less precise designation in Russian than in English. There were really only two “levels” of nobility in Russia outside of the Tsar’s family.
“Knyaz” was the highest level of the nobility. They occupied the position of dukes, marqueses and princes in other European countries but the title is translated as “Prince” and thus “princess.”
The boyars are usually translated as “Count.”