A diocese is not a regional office of a larger organisation, and the difference is the point of the whole structure.
In Catholic, Orthodox and Anglican understanding the diocese is the church, fully, in one place. Its bishop does not exercise authority delegated from a centre; he holds ordinary power in his own right by virtue of ordination and appointment to the see. What that entails is concrete.
- He ordains. Nobody below him can, which is what makes the office structurally indispensable rather than merely senior.
- He assigns clergy to parishes and removes them, within limits that canon law sets in the priest's favour.
- He erects, merges and suppresses parishes.
- He teaches with authority in his territory, and permits or withholds permission to teach theology in institutions there.
- He administers the diocese's property and its finances.
- He carries the liability. Decades of abuse litigation have established, expensively, that the diocese and not the wider church is the legal person that is sued, and diocesan bankruptcies in the United States follow directly from that.
What he cannot do is legislate against the universal church, ordain a bishop alone, or alter doctrine. The boundary between his ordinary power and the centre's is genuinely contested. Catholic teaching since the Second Vatican Council has emphasised the college of bishops as a body sharing responsibility for the whole church, and the practical relationship between that collegiality and the papal jurisdiction defined in 1870 has never been fully worked out. Orthodox and Anglican churches, having no comparable centre, locate far more authority in the diocesan bishop and in the synod of bishops of their own church.
The word itself is borrowed. In Roman civil administration a diocese was a group of provinces, and the church took over imperial geography wholesale in the fourth century, which is why so many ancient sees sit where a Roman provincial capital used to be.