The Difference Between A County And A Parish
The difference between a county and a parish lies in their origin and purpose. A county has always been an administrative unit, initially the domain of a noble and later of the people living within it. A parish is a local community of the faithful, normally entrusted to a parish priest or pastor under the authority of the diocesan bishop. Over time, the parish took on an administrative role as well, both in England and in one state that uses the term parish instead of county.
Counties

The word county itself has its roots in the Anglo-French word counte and the late Latin term comitatus, which translates to the jurisdiction of a county. It first came into usage in the mid 14th century in England to mean it was the region ruled over by a count or an earl.
The word count itself is a French word for a noble, which is similar in meaning to an Old English eorl. County had the same meaning as shire, which came from an Anglo-Saxon word for an administrative entity that was run by an alderman and a sheriff.

The National Association of Counties defines these administrative units as "acting as administrative arms of the crown or national government as well as the citizens' local government."
England used the terms both county and shire interchangeably, although county tended to be used more in official documents. The word shire was used more in the Anglo-Saxon period, but after the Norman conquest in 1066, the Normans largely replaced the term shire with county as befitting their own language and customs. However, some of these English counties had the word shire in their names, such as Hampshire, and locals would often use the term shire over county.
In 1634, by order of Charles I, the Virginia colony was divided into eight shires modeled on those of England. By the early 1640s, these shires had been renamed as counties, a pattern that most colonies would also follow. By 1790, there were 292 counties in the fledgling U.S., and more than 2,000 were formed between 1790 and 1900 to facilitate the administration of the western territories.

Counties are today the primary administrative unit for 48 of the U.S. states. They are governed by their state constitutions and offer law enforcement, health, social, and other services. Counties vary significantly in population from fewer than 60 residents in Loving County, Texas, to close to 10 million in Los Angeles County, California.
It is worth noting that the districts drawn for representation by the House of Representatives are not the same as counties, as these can be changed through redistricting and are based on population. Each district must have similar populations, while counties have no such limitations.
Parishes

Unlike counties, parishes have a religious origin. It comes from Classical Greek meaning neighbor, while Christian writers used the word paroikos to mean sojourner or having a temporary residence. This references the Biblical idea that Christians are to be travelers on earth, rather than calling it their home.
The word was also used for an individual group of Christians, led by a bishop, although etymonline states that it was used "in a more general sense" than the Greek word for diocese(dioikesis), which translates to district. By the 1300s, the word parish had taken on the meaning of a smaller administrative church zone within a larger diocese.
These parishes included a series of villages or towns, each with its own church and priest, which was in turn administered by a bishop. Many of these parishes tended to be located at politically important administrative centers, although actual borders could be difficult to maintain due to complex political situations in Medieval Europe.

The Council of Trent, which met over three periods between 1545 and 1563, formalized the parish. It required bishops to establish firm boundaries, live and pastor within those boundaries, and ensure that both doctrine and sacraments were administered by priests in line with Catholic teachings.
In England, parishes served a civil purpose as well, acting as the smallest group of the English government, handling property taxes, services, and planning. In America, there is one U.S. state that still uses parishes as an administrative unit, instead of counties: Louisiana.
Louisiana

Louisiana was settled first by the French in 1718 in a community known as Nouvelle Orleans(New Orleans). They controlled it until 1762, when they gave the territory to the Spanish, who would govern until 1800. Napoleon I briefly regained ownership of the territory, but sold it to America in 1803 along with vast swaths of the Western U.S. through the Louisiana Purchase.
Both France and Spain were Catholic powers, which gave colonial Louisiana a deeper Catholic presence and influence than the other territories that would become U.S. states. During this time, both countries organized the colony around ecclesiastical parishes, which served a dual role, both to keep the Catholic Church organized and as administrative reference points for the colony. When Louisiana entered the Union in 1812, it did so with 25 parishes on the map.
Initially, America made efforts to reorganize Louisiana around counties. The territorial legislature carved the region into counties in 1805, then created civil parishes alongside them in 1807, leaving the county mainly as a unit for elections and representation while parishes handled civil and judicial matters. Many residents of Louisiana resisted the term county, viewing it as a plot to replace their institutions with Anglo Protestant ones.
In 1845, a new state constitution was made, officially removing the word county entirely and declaring that parishes shall be the main electoral, administrative, and judicial division of the state. Today, the state has 64 parishes in total and remains among the most Catholic states in the country, with roughly a quarter of its residents identifying as Catholic, one of the highest shares in the South.
The key difference between counties and parishes
The key difference between counties and parishes is the original purpose of the organizational unit. While counties were secular, organized around a count or noble, parishes had a religious function. However, in the case of Louisiana, the term parish was a matter of tension, as the Cajun and Creole residents did not want their Catholic identity erased by the Anglo-Americans, and resisted the encroachment of the English term county.
Going further back, the term county itself represented a shift when the Normans conquered Anglo-Saxon England and replaced the term shire with their own term county. This demonstrates the complicated and at times contentious meaning and usage of words, especially when it comes to governance.