The two tools do different jobs
Booking software fills the calendar. A coaching CRM holds the relationship. They sound similar because they both touch clients and sessions. The work they do is not the same.
Booking software turns a link into a slot. The client picks a time, the calendar updates, the reminder goes out, the payment is taken. Its job ends when the client walks in.
A coaching CRM starts where booking ends. Who is this person, what have we worked on, what did we cover last time, what did they pay for, what is outstanding, when did we last speak. Its job is the client, not the calendar.