There's a difference, you see. A Monk or Nun typically lives to a greater or lesser degree secluded from the world, having devoted their life to God in order to pray and meditate on the scriptures. In Buddhism, there is not the same emphasis on seclusion. The terms "Monk", "Monastic" etc are Western, English ideas that do not apply. The root of the word "Monastic" is greek, and means to live alone, apart. The implications are that to be a monk, you need to live separate from the laity.
Since Buddhist clerics do not separate themselves from the Laity, but instead make daily rounds and make themselves available whenever possible to the general public, in order to do things like performing blessings, giving advice, and so on, their role is closer to that of a priest.
The lines have been somewhat blurred in recent decades since Christian monks and nuns are less secluded than they were, but nevertheless, the distinction holds. Jiho Sargent ought to know - she's a priest in Tokyo's largest Zen Buddhist temple, and has been for many years.