In most cases (there is always one bad apple) a Private Banker is a more qualified individual, with some experience in handling the more complicated issues that a person of higher affluance would have. I.E. The need for trust services (normally on referral to trust specialists) investment management, IRA management, estate issues, jumbo home loans, etc. These clients would be also be some of the bank's major income earners on both deposits and debt, warrenting the extra service a Private Banker would provide (and covering the higher salary the Private Banker would expect to make). In a nutshell, Private Bankers are much more service oriented (and I mean GOOD service) than a Personal Banker you'd find in a branch.
As a Personal Banker I would expect a variety of descriptions apply. Many do basic account openings, some business products, some lending, etc, based on their skill level. Some portfolio management is also involved, but not for 100% of their clients as a Private Banker would do. Limited knowledge base is acceptable for a personal banker and while referals are generated to other areas of the bank, they aren't your top 10% money making clients when judged on an individual basis.
As a Private Banker, when I was called and asked to draw $100M out of their account in the form of a cashiers check AND to run it down to the county court house so they could buy a home at auction I said...What time and do you want a latte' while you wait for your auction to come up?
As a Personal Banker I explained the ease of coming to the bank to get a cashiers check, and asked if they'd pick up a cup of coffee for me on the way