What services are typically offered under private client banking?

It offers slightly bespoke banking and investment products that are otherwise not available to the general banking customers. You get more attention to start with. Like having your own financial planner, concierge services, etc. Even simple things like the visit to the bank or the telephone call or email are handled by a completely different set of personnel, who are trained to give you attention and priority.

These obviously are all fluff.

The main differentiator is where the bank and its network can take benefit of various tax amnesty schemes or tax saving schemes whilst still having custody to your money. Investing it in products that have a minimum threshold to apply, etc.

These benefits are not extended to the general public. They are meant for HNWI and most of such investment classes are in the derivatives market, where the bank and its investing partners have a much stronger sense of the investment risk and return.