The role of a generalist T&L Coach is relatively new. This type of role was usually more common in Elementary School, focusing on Literacy. Then we had a variety of terms to define a Technology Coach, or Tech Integrator / Coordinator, etc.
A generalist T&L Coach is a specialist in teaching and learning strategies, able to support any subject area. Consultants that are more focused on student-centered coaching include: Diane Sweeney (https://dianesweeney.com/), Jim Knight (http://http://www.instructionalcoach.org/), Elena Aguilar (http;//http://elenaaguilar.com/)