Each Business Profile is recognized separately, even if the Business name is the same. Each one has its own Staff, Service Menu, Schedule, Availability, and more. This includes Clients as well.
Even if it's the same Client, records across Business Profiles are independent of one another and cannot be linked. If you work with a Client at Business A and Business B, the Client will have one record at Business A and another at Business B. Record A will store all activity for Business A and record B will store all activity for Business B.
On the flip side, that Client can use their same MassageBook account to book online at both Business A and Business B. When the Client signs in to their own account, they will see and can manage booking activity for both.
If you are adding a Business, you can export your Clients from Business A as a CSV file and then import that list into Business B. Only contact information in the Details section of a Client's record will transfer though; Activity, Credits, SOAP Notes, Intake Forms, etc. will not.