Hi PaulH-1052,
The dedicated database server option is for a dedicated machine with only the instance of SQL Server dedicated for RD Services and it will create a database automatically; the Shared database server option is for a new SQL Instance on an existing install with other Instances and you need to manually create an existing database on SQL Server. In addition, dedicated database server option used windows authentication, but shared database server option used SQL Server authentication.
For more details, please refer to:
Remote Desktop HA Connection Broker
RD Connection Broker High Availability
Best Regards,
Amelia
=======================================
Please remember to click " Accept Answer" and upvote the responses that resolved your issue.