Answer:
In the Catholic Church a Diocesan Bishop confirms, ordains Priests, administers a diocese, preaches the Holy Gospel, performs visitations of monasteries, convents, and seminaries, instructs the faithful in sound doctrine, and performs other Priestly duties as well.
An auxiliary Bishop of a diocese does whatever work he is instructed to do by his diocesan ordinary (the Bishop of the Diocese).
Bishops directly in the service of the Holy See serve in the offices of the Roman Curia, oversee certain Apostolic works, or can be employed in diplomatic service, such as Nuncios of the Holy See to various countries.