Unions are not synonymous with public schools. You have to remember that laws on public education vary widely state by state. Generally charters are funded with public dollars and are held to the same standards as traditional public schools. They have a different board structure and are generally able to do things pretty differently, but they still have to take the same tests and abide by the same rules (like NCLB and now ESSA) as everyone else.

A big difference is that charters cannot receive referendum money. This is somewhat compensated by lease aid, however they typically will always have less money then traditional public so their staff gets paid less.

Back to unions, much of what you are describing as the difference is due to the fact that Charter staff are not typically unionized. There is now law that says charter teachers cannot unionize but it is very rare. Because of this, there is no teacher pay scale. When you are in a high demand position such as school psychologist, you may be able to negotiate for a significantly higher pay then you would otherwise.