Difference between public and private service?

Public services are often financed via taxation while private services are based on the user pays principle. Public services often cater for larger groups while private services are often for smaller numbers - this is true for educational services for example. In terms of transport, taxis are private while buses tend to be public - one offers a small scale more personalised service the other a scheduled, predictable service along a fixed route.
Public services have a clear line of political accountability while private operators are more often regulated by market forces in terms of price and service quality
and range.