Probably there are some persons more knowledgeable about this subject.
After the Norman Conquest in 1066, there were a number of Saxon revolts which William the conqueror crushed. William confiscated the lands owned by Saxon nobles and gave them to his Norman and other followers as fiefs. Technically King William owned the land in those fiefs and his tenants had to pay rent in the form of feudal services to keep those fiefs. The king could and did confiscate fiefs as punishment for disloyalty.
Lords of fiefs, who were vassals of the king, could make smaller fiefs of parts of those fiefs and grant them to men to serve as the vassals of those lords. That process was called subinfeudation.
Lords who were directly vassals of the king of England are called tenants-in-chief, and a group of the most powerful one hundred or so of those tenants-in-chief were called barons. This is a somewhat different meaning than the meaning of baron in the Holy Roman Empire and some other realms but the question is only about the UK.
In Anglo-Saxon England (5th to 11th centuries), earls had authority over their own regions and right of judgment in provincial courts, as delegated by the king. They collected fines and taxes and in return received a "third penny", one-third of the money they collected. In wartime they led the king's armies. Some shires were grouped together into larger units known as earldoms, headed by an ealdorman or earl. Under Edward the Confessor (r. 1042–1066) earldoms like Wessex, Mercia, East Anglia and Northumbria—names that represented earlier independent kingdoms—were much larger than any individual shire.
William the Conqueror restricted the sizes of Earldoms to individual shires in England and limited the powers of Earls in other ways. Some Earls regained much power during the Anarchy of 1135-1154, but their powers were restricted again by later kings. The shire reeves or sheriffs, appointed officials, gradually took over most of the functions of the earls, who gradually became hereditary, in their shires. Thus Earls lost the connections to the shires mentioned in their titles, and many earls came to have their principal landed estates in other shires.
As far as I know, the titles of Baron and earl were the only noble titles in England for most of the Middle Ages, and the only ones who possessors originally had a connection the lands mentioned in their titles, a connection which gradually became less and less important.
When parliament developed in England in the 13th and 14th centuries earls and barons gradually acquired the hereditary right to be summoned to the House of Lords (along with bishops), and when other noble titles were introduced later the possessors of those titles also had the right to vote in the House of Lords.
The titles of earl and baron developed in a roughly similar way in Scotland, although I think that in Scotland a baron held a feudal barony without the right to vote in parliament, and a lord of parliament was the equivalent of an English baron.
A number of other noble titles developed in continental Europe before being granted by kings in Britain, usually without any lands attached in Britain.
The two most important titles, count and duke, developed from both Roman and Germanic origins. A count is a comes in Latin and a Graf in German. A duke is a dux in Latin and a Herzog in German.
The title of comes was given to companions of the emperor and later to generals commanding a mobile army force. The germanic tribes had a title of Herzog or army leader used by war leaders. In late Roman times a dux was a general commanding static frontier defence forces in an area, as opposed to the mobile field army of a comes. Late in the history of the western Roman Empire, officials were put in charge of each city state in the empire, with the title of comes.
Barbarian kingdoms which took over the western Roman Empire tended to keep that system, with officials with the titles of comes in Latin and Graf in Germanic administering city states, and officials with the Latin title dux and the Germanic title Herzog being in charge of military affairs in large regions.
A count had to lead the gGermanic warriors of his city state or county when they were summoned to war by the king, and a duke was in command of all the warriors in his territory in time of war, so that implied that Dukes could command counts.
In the Carolingian era a system of feudalism developed, where each Germanic warrior rented one or more country estates as a fief from the government, and owed military service as his rent. He used the income from his estates or manors to pay for his expensive armor, horse and weapons. The holder of a manor was called the lord of the manor and had extensive rights over the inhabitants of it.
So when a feudal army went to war it would include lords commanded by counts commanded by dukes commanded by kings.
And as time when on the various lords of manors made their fiefs more and more hereditary and came to become vassals of their counts, who tended to make their fiefs hereditary, and to become vassals of their dukes who tended to become hereditary and to be vassals of their king.
So the warriors of a fully feudal kingdom would be thousands of lords of manors who were vassals of their counts who were vassals of their dukes who were vassals of their king.
But since feudal lords, counts, dukes, and kings could own many different estates and manors, and tended to acquire more over the centuries, the hierarchy could get very complex, with lords being vassals of two or more different overlords who might go to war with each other. It was possible for two different lords to be each other's overlords for different fiefs, and for someone to be their own overlord of some fiefs.
A baron was a lord who was a direct vassal of the King instead of being a vassal of a count or a duke.
One rank that developed in the Kingdom of the West Franks or France was vicomte or viscount, a deputy of a count. If was originally an appointed official position and gradually became a hereditary position.
Another feudal rank was the French Marquis, from the Germanic Markgraf, a count of a border region who had to defend it and so was more important than a regular count.
In the Holy Roman Empire the princes of the Empire were important nobles directly vassals of the King and Emperor. The princes had several different titles, ranking from lowest to highest as princely count, landgrave, margrave (Marquis), count palatine, prince, duke, and the rare grand duke and archduke.
Since an English earl was considered to be equivalent to a count, the English kings never granted titles of count.
In the 14th century English Kings began granting European titles to members of the royal family and to nobles and powerful, wealthy commoners. These titles were often given to men with little connection to the territories named in the titles.
In England the first viscount title, above baron and below Earl, was granted in 1440, and the first in Scotland in 1606. The first English title of Marquess (Marquis) was granted in 1385. In England the first royal duchy was created in 1337 and the first non royal dukedom in 1397. In Scotland the first royal dukedoms were created in 1398, and the first non royal dukedom in 1488.
In recent centuries several successful generals have been granted victory titles naming the places of their victories, even though those places were not within the United Kingdom. So there is definitely now no necessary relationship between properties owned or places resided in and the places named in a noble's title.
As for peer and peerage, in the UK a peer used to be the possessor of a noble title with a hereditary right to sit and vote in the House of Lords, but since the 1990s the government choses which of the nobles are members of the House of Lords.
The meaning of peer in the UK is now defined as:
in the UK, a person who has a high social position and any of a range of titles, including baron, earl, and duke, or a life peer:
a member of any of the five degrees of the nobility in Great Britain and Ireland (duke, marquis, earl, viscount, and baron).
Other countries have had peers, whose attributes were not identical with those of British peers.
The hereditary title and position of Peer of France (French: Pair de France) was held by the highest-ranking members of the French nobility. It first appeared in the Middle Ages, was abolished in 1789 during the French Revolution, reappeared in 1814 with the Bourbon Restoration, and was definitively abolished in 1848.
French peerage differed from the British peerage, a more general term. The vast majority of French nobles, from baron to duke, were not peers. The title was an honor granted only to few dukes, counts, and princes of the Roman Catholic Church, analogous to Grandee of Spain.
And maybe some other countries still have peerages which resemble and differ from the British and French peerages in various ways.