The best site and forum around for information regarding the Royal Irish Constabulary (including the Black and Tans and the Auxiliaries) is run by Peter "McRIC" :
The Royal Irish Constabulary was an armed police force that operated through most of Ireland. The Dublin Metropolitan Police (DMP) operated in Dublin (though the RIC had a depot in Phoenix Park) and were unarmed generally. G Division of the DMP were plain clothed and were an intelligence operation.
The Black and Tans were elements of the standard RIC that were recruited from outside Ireland to make up for the loss of regular RIC members through resignations, wounding and killed. They were generally ex-servicemen who had fought in the Great War. They were not recruited from British jails; this is a myth. Many were in fact Irish Catholics. They were integrated with the standard RIC but did not receive the same training or discipline.
The Auxiliary Division Royal Irish Constabulary (ADRIC - or Auxiliaries) were a separate unit within the RIC that operated in companies around Ireland. Generally these were ex-officers and many were highly decorated.
It was (and still is) common to call Black and Tans as Auxiliaries and vice versa. Generally, Auxiliaries operated as independent groups. Black and Tans operated by and large with ordinary RIC. Either way, they operated very differently to the RIC and in many instances, operated outside of the law that they were supposed to uphold.
At the end of the War of Independence, many Auxiliaries went to Palestine to continue their brand of police work. Many RIC were assisted to emigrate to other parts of the British Empire.
Book on the subject include :
Black and Tans by Leeson
Black and Tans by Bennett