a parish is a county. I do think Orleans parish includes all of New Orleans but I don't think it includes anything else. The parish president is like a county executive. I think the pop of NO is about half million and the metro area is alot larger but I don't really know.
The parish word just comes from the french catholic settlement.
Civics 101:
In the 21st Century, a Louisiana parish is, in fact, roughly equivalent to a county in other states. Parish is originally an ecclesiastical (church) term. In French and Spanish, Roman Catholic, Louisiana, records were kept by the church parish. Eventually, the term was applied to a civil division of the state, as well. In colonies, such as Virginia (which had a "state" church, the Church of England), each colony was divided into counties; and each county was then subdivided into ecclesiastical (church) parishes for purposes of levying taxes...thus, a county could be comprised of several parishes.
The entirely urban City of New Orleans and Orleans Parish are co-terminus, that is, they have the same boundaries and the same government.
Elsewhere in LA, Baton Rouge is the principal city in East Baton Rouge Parish, and there is a unified "City Parish" government that rules all of the Parish.
Other parishes, such as Jefferson, which includes the City of Kenner, and other unincorporated areas such as Metairie, are not part of the City of New Orleans (or Orleans Parish). They have a unified government under an elected "Parish President" who rules over the entire Parish. They are generally considered to be part of "Greater New Orleans" as they are really suburbs of New Orleans; but, their government, their services, their tax base, etc. are entirely separate from the government, etc. of New Orleans.
The population of New Orleans (City and Parish) in the 2000 census was 484,674. In 1960, the population was 627,525. New Orleans lost 142,851 people between 1960 and 2000.
New Orleans used to have the dubious distinction of being at the top of the list for the U.S. murder rate. They suddenly were no longer mentioned in the list. The reason for this is not because there were fewer murders ... but, because in the 1990 census, the population (496,938) dropped below the half million population required to be considered for the list.
It will be interesting to see what the population of the City will be in 2010. They have 4 years to rebuild.