Differences between "fortification nouns"
This is one of the cases where English has a bunch of words that mean very nearly the same thing because of its many overlaid mass borrowings from its neighbors, and in this case also because of the rich and ancient tradition of warfare in Europe. If you pick the wrong word, native speakers will still understand, but they may get slightly the wrong impression. Don't worry about it too much.
I'm going to explain the words in a slightly different order than you listed them.
A fortification is any structure whose primary function is to aid a military defense. It is most often used for structures whose only function is defense, such as city walls, trenches, tank barriers, etc. Fortifications might not be permanent structures; the trenches of World War I were dug as needed and filled in when no longer useful. There's a related verb: you fortify something when you prepare to defend it (not necessarily by erecting fortifications). This term is in current usage.
A fort is a building or group of buildings designed to serve as a base for an army. It also serves as a fortification in the above sense; it may for instance have artillery emplacements, walls designed to resist cannonfire, etc. This term is also current, but is fading out of the language in favor of "[military] base", partly because traditional fortifications are less and less useful in modern warfare. Forts often have names: "Fort Pitt", for instance, is the name of a fort (built in the 1730s and now almost entirely gone) near where I live.
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Fortress, castle, citadel, and stronghold are all roughly synonymous with fort. There are, however, differences of nuance:
- A castle is or was the home of a feudal lord, as well as being a fort. Therefore, people still build forts, but nobody builds castles anymore, except as a deliberate anachronism, e.g. Cinderella Castle at Disney World. The word is sometimes applied to particularly fancy estates to suggest that the person who lives/lived there is acting like a feudal lord, e.g. Hearst Castle; in this case the building(s) in question need not be defensible.
- Fortress and citadel are older synonyms for fort and castle respectively. They suggest that the building so described is larger, more impressive, and harder to attack than a simple fort or castle. (Citadel originally referred to a fortress "commanding a city, which it serves both to protect and to keep in subjection" [OED], but modern usage does not reflect this.)
- Stronghold can technically be used for any well-defended place whether or not built for the purpose, but actual usage is basically the same as fortress.
Finally, a palace is the home of a monarch or other high-ranking feudal lord (a duke or a prince, perhaps). It is not necessarily a castle, and in fact often deliberately not a defensible fort (consider Versailles). By extension it is sometimes used to refer to any large, ostentatious, expensive dwelling. This word is in current usage.
Etymologically, fort, fortress, and fortification are all from the French root fort = [place of] strength; palace and citadel are also from Norman French palais, citadelle; castle was borrowed directly from Latin castellum and then reinforced by Norman French castel (which became château in Modern French); and stronghold is Old English, a composition of strong + hold.
Other related words include:
- keep the central, most-defensible part of a castle or fort.
- hold any fortified dwelling or place of refuge. This noun is basically never used in Modern English except by writers of fantasy.
- arsenal a fort whose primary purpose is to store weapons, and/or a naval dockyard.
- manor [house] the unfortified home of a minor feudal lord.
- fastness Old English equivalent of fortress, also basically extinct in Modern English; the OED doesn't trace the etymology back far enough for me to confirm my suspicion that this sense of fast is the Germanic equivalent of fort.
- garrison originally equivalent to fort, now refers the body of troops assigned there.
- bunker modern military jargon, a mostly-underground fortification designed to protect people from aerial bombing.
In America, if you ask someone what a fort is, chances are he will tell you, "Well, it's an enclosure made of wood that affords some measure of protection against enemies, as in the 19th century when American soldiers and settlers gathered inside the fort to protect themselves from attacks by Native Americans ("Indians").
Fort comes from the Latin word fortis, meaning strong. A fortification is a strong structure that protects. It need not be made of wood, but it could be made of metal, brick, concrete, rocks, boulders, timbers, or a combination of some or all of these. It is a generic term for a protective structure of some sort.
A fortress is a protective structure, but it has the connotation of being massive, imposing, exceedingly strong, and difficult to penetrate. Martin Luther's most famous hymn is "A Mighty Fortress Is Our God, A Bulwark Never Failing."
A stronghold also affords protection from enemies, but the word is used more commonly to denote a temporary protective measure. A stronghold is, by connotation, not as impenetrable as a fortress but can be abandoned, if necessary, when it becomes compromised. Interestingly, some bad habits and addictions can be described as strongholds in people's lives, but these strongholds can be brought down and defeated through diligent effort and through the support of a network of helpers, particularly recovering addicts who hold the addict accountable for his recovery.
A citadel is also a fortress, but it is designed to protect the residents of a city from besiegement by an enemy force. It could take the form of a thick wall that surrounds the center of the city, with such features as a bastion, a rampart, ravelin, glacis, and more.
For a great diagram of a castle, see http://www.allcrusades.com/CASTLES/GLOSSARY_OF_CASTLE_TERMS/glossary_of_castle_terms.html A castle is a permanent fortification and is thought of, traditionally, as the residence of royalty--a king and/or a queen. Soldiers and guards inside the castle serve the royal family by providing protection from attack. A host of employees and/or servants work and perhaps live within the castle's walls, and serve as tradesmen, cooks, bakers, scullery maids, groomsmen, merchants, clergymen, and other service providers.
Some castles have a moat, which is deep, wide trench, usually filled with water, surrounding the rampart of the castle; a drawbridge that links the castle to the barbican by spanning the moat in the down position to allow people in and out, and preventing entry to the castle when in the up position; a chapel for religious rituals; a dungeon (or dunjon), the heavily fortified central tower or keep, which serves as a fortification and possibly as a jail for criminals.
Finally, a palace is also the residence of royalty, and in addition to being constructed so as to offer protection to the royalty and citizenry inside, a palace's architecture is more elaborate and aesthetically appealing than that of a castle, which while attractive in its own right is designed primarily with protection, not beauty, in mind.
When people think of a palace, they might automatically think of the Palace at Versailles in France, which was built in the 17th century for Louis XIV in the southwest section of Paris (near Versailles). This palace, like many others in Europe, comprised elegant rooms and halls, decorated and furnished extravagantly with chandeliers, intricate woodwork, rare art (e.g., paintings, tapestries, sculptures, statues), and every conceivable creature comfort for the royal family, who was attended to by courtiers and servants galore.
Practice will vary by region and military tradition. I'll give you my take.
fort is an outpost, suggesting removal from the main military presence.
fortification is built on an existing structure (building or village) or advantage in terrain (i.e. a hill or cave); it suggests being less remote, but also ad hoc. "They fortified the hill with a stone wall." It represents a militarization of an existing thing.
citadel is a military center, suggesting a city (same root word), training ground and many people.
stronghold suggests a cache of supplies and/or a prison. In English tradition, a "keep". It isn't the center of power, but when pressed you could run to it and hold out until reinforced. I.E., you could take a prisoner there without the townspeople breaking them out.
fortress is a highly defensible position prepared to withstand seige. This is a military bulwark against opposing military force.
castle is essentially a fortress-residence. Unlike the other places you might house soldiers or supplies, somebody lived here, typically the feudal lord with territorial rights for the surrounding area, making it a political and administrative center.
palace is a fortress-residence for royalty.
A fort or fortress is a building whose purpose is purely military.
A fortification is also purely military, but might not be a building. It could just be a fence or "palisade" around some area, or trenches in a field, or a wall across a field.
A stronghold is any well-defended place. Maybe a building, maybe a cave, maybe a whole country.
Citadel, I had to look up, but it is "a fortress that commands a city and is used in the control of the inhabitants and in defense during attack or siege." (Dictionary.com)
A castle is a defensible structure that's also used a place to live, for example by a knight or noble.
A palace is a living place for a knight or noble, with no connotation of military value or capability for defence.