Private banks are banks owned by either an individual or a general partner(s) with limited partner(s). Private banks are not incorporated. In any such case, the creditors can look to both the "entirety of the bank's assets" as well as the entirety of the sole-proprietor's/general-partners' assets.
There were many private banks in Europe, but most have now become incorporated companies, so the term is rarely true any more. Today, the term "private bank" can also refer to the financial institution specializing in financial advice and services for high-net-worth individuals (private banking).
"Private banks" can also refer to non-government owned banks in general, in contrast to government-owned (or nationalized) banks, which were prevalent in communist, socialist and some social democratic states in the 20th century.