Regular Public Transport (scheduled service)
These are flights between fixed ports, based on a published timetable and tickets are open for the public to purchase. Operators are required to be licenced to operate RPT by CASA (or relevant body) and have systems and programs in place to meet the RPT standard.
Subsidised RPT
This is RPT but where a government body or company agrees to purchase X seats on every flight (regardless if that many people actually fly) or over a group of flights. This is done particularly on routes which may not be profitable for an operator.
Charter
A person or company pays an operator to operate the flight from A to B. They are essentially hiring the entire aircraft and its crew. Tickets are not sold by the operator, and flights are generally random and not to a published schedule. The person or company paying determines the passengers, cargo, etc.
So as Ash said, it depends a lot on the context.
As a passenger you may not notice a lot of difference. From an operational perspective, the crew flight the aircraft the same way. It is more behind the scenes where the differences are and on the commercial side.
Conceptually there is no difference between domestic and international charter. However, most bilateral agreements do state that an operate can only operate a certain number of charter flights between certain countries/ports before they must apply for rights under the agreement (ie: become RPT).
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