I am guessing that the Russian sense of seminar is analogous to a recitation or tutorial in Anglo-American universities.
In the lecture + recitation classroom format, class time is divided between two types of meetings: a large group, the lecture; and a small group, which may be known as recitation, section, tutorial, workshop, seminar, review, or discussion among many others— the terminology varies not only by country, but in North America, by institution and indeed by department and instructor. In the lecture, the instructor delivers a presentation to the entire class. It is not interactive, as the audience may number in the thousands. The small group, however, is designed to be interactive, and as there may be only 10 or 15 students in each, there is time to discuss the lecture or the texts, ask questions, review exam answers, and so on.
In U.S. higher education, the leader of the small group is usually referred to as a teaching assistant, or T.A. for short. The T.A. is usually a graduate student (hence the alternative term graduate teaching assistant), and the teaching assignment part of his or her program. Occasionally, the terms facilitator or section instructor were used at my university, and where the small group was a laboratory session, lab instructor.
In the U.K., I believe tutor is the usual term for this role.
We did have courses known as seminars, in which there is no lecture, and the course instructor (usually a professor) himself leads an interactive discussion among 5-15 students. We had no special word for the instructors of such courses.