What a coaching CRM is, said simply
A CRM is just one place that holds every client you work with, the history of what you have done together, and the money that flows between you. For a coach, that is the back office. Clients, sessions, notes, payments.
Most CRMs are built for sales teams. They assume a pipeline of leads, a deal that closes, a customer who churns. Coaching does not look like that. A coaching relationship is a long arc. The same client for one year, three years, sometimes a decade. The right CRM for a coach is shaped around that arc, not a sales funnel.