Sensei is the ordinary Japanese word for teacher, used of schoolteachers, doctors and martial-arts instructors as much as of religious figures, so it is a broad term of respect rather than a defined religious office.
A general honorific
The word is applied to anyone who teaches or who holds a knowledge or skill worthy of respect, a schoolteacher, a physician, a master of a craft or a martial art, and in the religious context a teacher of Buddhist practice, so its use is wide and its religious sense is only one among many. Applied to a Zen or other Buddhist teacher, it marks the person as one who instructs students in practice, but the word itself carries no specific rank or authorisation, being a general term of respect for a teacher.
Sensei and the deeper title
In Zen the word sensei is sometimes used for a teacher who guides students, distinguished from the more elevated roshi reserved for the most venerable masters, but the terminology is not fixed and varies between lineages, so the title should not be read as a precise office in the way that dharma transmission is a precise event. What gives a Buddhist sensei genuine authority is the training and, in the Zen case, the transmission that stands behind the person, not the honorific itself. The word thus belongs with the general terms of respect for teachers rather than with the defined offices of a tradition, and its breadth, spanning the classroom, the clinic and the meditation hall, is exactly the point to grasp about it.