Why Some States Call Them Parishes And Boroughs
Of the 50 states, 48 are organized around counties, but two use a different administrative term. Louisiana uses the term parishes, while Alaska prefers boroughs. They are called parishes and boroughs due to their culture, history, and values, which sets them apart from the other 48 states.
These are not informal arrangements in Alaska and Louisiana, but are enshrined in their respective state constitutions. Both of the terms also have a history prior to the establishment of the U.S.
What are parishes and boroughs?

The word parish traces back to the Greek paroikia, from paroikos, one who dwells beside or near a house. By the early Christian period, it had taken on a different meaning. Christians used it to mean sojourner, echoing themes from the New Testament that Christians were to be merely travelers on Earth rather than treating it as their home.
Parishes also held a secondary meaning for Christians, of a geographic area of believers with a single bishop presiding over them. The term was formalized in the fifth century, following the legalization of Christianity in the Roman Empire.
The primary purpose of these parishes was to keep churches organized, but they were also useful as administrative centers, such as in Anglo-Saxon England. During the Council of Trent in the 16th century, the Catholic Church laid out stricter guidelines for parishes to ensure bishops taught approved Catholic dogma and doctrine, as a counter to the Protestant Reformation.
The word boroughs meanwhile, comes from a Proto-Germanic word known as burg, referring to a fortress or fort on a hill. It could also be synonymous with castles in High German or Old Norse. Within England, the word began to take on a different meaning, as the Domesday Book from 1086 used the term burgus to mean a town.
England developed different versions of boroughs, such as judicial boroughs or taxation boroughs. Others were given more privileges through parliamentary boroughs, meaning they could elect members to Parliament.
By the time of the Industrial Revolution, many of the old boroughs had become depopulated due to residents moving to the city for work, leading to overrepresentation in Parliament. To handle this issue, Britain passed the Reform Act of 1832, which disenfranchised the "rotten boroughs" and handed seats to the new industrial towns.
In America, meanwhile, borough was used to mean an incorporated town.
Why does Louisiana have parishes?

Louisiana has parishes due to its history of Catholic settlement. In 1718, the French established the first European settlement in Louisiana known as Nouvelle-Orleans, or New Orleans.
France governed the territory until the Seven Years' War, when it secretly ceded Louisiana to its ally, Spain, by the Treaty of Fontainebleau in 1762, a transfer made public in the Treaty of Paris a year later. Spanish officials did not establish firm control until 1769. By that point, the French had already established the parish system, managed through the larger diocese in Quebec, Canada. These parishes played a role in administration as well due to their resources.
Spain continued this trend of parish-based administration until France reacquired Louisiana in 1800. Napoleon Bonaparte planned to use the territory as a breadbasket for a new empire in the Americas, centered on the sugar colony of Saint-Domingue.
However, he would abandon this project after his expedition failed to put down the Haitian Revolution, and with war in Europe looming, he needed funds. He sold all of French Louisiana to America through the Louisiana Purchase in 1803.
The Americans initially imposed their own system. In 1805, the territorial government carved the Territory of Orleans into 12 counties, using boundaries and names borrowed from the old church parishes.
Two years later, on March 31, 1807, the territorial legislature created 19 civil parishes on top of those same ecclesiastical boundaries without abolishing the counties. That left a dual system in place where counties handled elections and territorial taxes, while parishes took over civil, criminal, and probate matters.
By the time Louisiana entered the Union in 1812, it had 25 parishes. The first state constitution of Louisiana in 1812 used the term county as an electoral division, but it also included the term parish. However, the French Acadians who lived in Louisiana continued to use the term parish, in part to resist being absorbed or sidelined by the new, largely Protestant American settlers.
By 1845, Louisiana passed a new state constitution but no act ever formally abolished the counties. The 1845 document simply dropped every reference to them as a civil or legislative division, leaving parishes as the state's only administrative unit and no references to churches made.
Today, Louisiana has 64 parishes. The law code of these parishes is unlike that in the rest of the U.S. where Louisiana relies on a civil law tradition inherited from its French and Spanish colonial codes, rather than the common law tradition used in the other 49 states.
Why does Alaska have boroughs?

Alaska chose boroughs over counties when it wrote its constitution, a conscious decision on the part of its delegates and residents to enable maximum local autonomy.
In November 1955, 55 delegates from across Alaska gathered in Fairbanks to create a state constitution. They also involved the local populace, taking a recess in December to discuss the proposed document with citizens and receive feedback, before ultimately signing the state constitution on February 5, 1956. Voters ratified it that April, and it took effect when Alaska entered the Union on January 3, 1959.
The term county was discounted for several reasons. The first was to avoid overlapping tax jurisdictions, which Article X of the constitution directly states. The second was to prevent legal precedents from court cases involving counties in the rest of the U.S. being applied to Alaska's administrative areas.
The third reason was to enable "maximum local self-government with a minimum of local government units," as stated by Section 1 of Article X of the Constitution. This was necessary due to both the size of Alaska, which is more than double the size of Texas at 663, 268 square miles, and its isolated communities, including Native Alaskans living in small villages.
Lastly, on a more practical level, Alaska is far more sparsely populated than most states. The 1960 census, the first after statehood, counted just 226,167 residents across the entire state. Most of its regions simply did not have the population to warrant a county-scale government.
Turning the constitutional principle into actual local governments took years. The Borough Act of 1961 defined the whole state as a single Unorganized Borough, out of which organized boroughs could be carved.
Bristol Bay was the first to incorporate but adoption was slow enough that lawmakers passed the Mandatory Borough Act of 1963, forcing eight populated areas, among them Anchorage, Fairbanks, Juneau, and Ketchikan, to form boroughs by the start of 1964.
Alaska now has 19 organized boroughs, the newest being Petersburg in 2013, while the Unorganized Borough still covers roughly 323,000 square miles, more than half the state's land area, and is administered directly by the state.
Parishes and boroughs are more than just names
In theory, one could say that parishes and boroughs are county equivalents, as they both serve as administrative divisions. However, they each point to a deeper history and culture.
In the case of Alaska, boroughs point back to old English days of local town leadership, and a desire to maintain as much local autonomy as possible.
Parishes, meanwhile, harken back to Louisiana's founding as a Catholic colony and the preservation of a unique culture that is still a prominent feature of Louisiana. By continuing to use parishes and boroughs, Louisiana and Alaska maintain their state's culture on opposite ends of North America.