Tutoring is direct, one-on-one instruction that typically supplements instruction. A tutor will help a student, away from class, to improve in one or multiple subjects.
Learning coaches are much more like full-time teachers, but the methods vary significantly. Oftentimes coaches will instruct on multiple subjects, and will remain with a student through multiple school years, rather than advancing the cohort each year. Learning coaches create personalized learning plans and guide students through the entire curriculum, but the students do the driving according to their interests and abilities.
Coaching can consist of reading, writing, presenting, Socratic discussions, eLearning, and project-based assignments. Very rarely do coaches give direct instruction or lecture. Coaching encourages much greater agency, pushes students to become self-directed, and develops time and task management skills at an early age.