In my novel, the world is made entirely out of islands, but I don’t know how to explain this without using the word islands. In that world, there are only islands so they are just called countries. Now how should I tell the reader that world is made up of islands?
Keep it simple:
An island is still an island, since a country could be part of an island, or several islands. Don't confuse the issue by using clever, cryptic language. If you never refer to anything but islands, they'll get the point. Or the world can have a suggestive name like Islandia.
Characters can discuss the island-like nature of the world, or discuss a mythical land with a titanic island where it goes on and on with no ocean visible. They lack the words to describe it, referring to the idea as a "super-island."
I recommend that you make the language(s) in your story have separate words for islands and countries, and if your story is written in English have the characters use the English words "island" or "isle" on one hand and "country", "realm", "state", "nation", or "polity" etc. on the other hand. And only rarely have them use the words in their own language, when the meaning is clear in context.
And as for showing there are no continents in the world, maybe someone is impessed with how large an island is after sailing along its coast for days, and someone else can say that there are a few islands even larger than it. And if asked they can say the largest land in the world is Grasprok Island which has an area of about 100,000 square miles, or something. That will show that there are no continents on that planet.
An island is a geographic feature.
A country is a region or area in general meaning and more usually and more specifically a nation state with a specfiic region and usually with a majority of the population being of one ethnic group and speaking the same language, and with a single independent sovereign government over the whole of the country.
I see no reason to combine or confuse a geographical feature like an island and a political entity like a country, no matter how much they might occupy the same location.
There are three possible relationships between islands and countries, and there are a number of different examples of all three of those possible relationships on Earth.
one) Iceland is a country consisting of a single island, and an island containing one country.
Two) The Bahamas are an archipelago of many islands all part of one country, and a country consisting of all the islands in the archipelago.
Three) Hispaniola is an island containing two countries. The Dominican Republic and Haiti are two countries which are each within part of Hispaniola.
Here is an example of a combination of Two) and Three): New Guinea is an island containing the country of Papua New Guinea and part of the country of Indonesia which contains all or parts of many other islands.
If your fictional world contains many islands and many countries, it is not certain that every country will be a single island, or that every island will be a single country. In fact, it seems quite likely that it will have multi island countries and multi country islands.
I note that before the era of colonialism, some large islands, like the continents, each contained tens or hundreds of separate countries.
And if the islands in your world are not all very tiny (and thus likely to beparts of the same country as neighboring islands) they are likely to contain rivers and lakes.
And what do rivers and lakes contain, beside water and fish?
River islands and lake islands.
Majuli, in the Brahmaputra River in India, a non-coastal land mass between two channels of one river, is recognised by the Guinness Book of World Records as the world's largest river island, at 880 km (340 miles).1 Britannica cites another large land mass, Ilha do Bananal, in Tocantin, central Brazil, as an island that divides the Araguaia River into two branches over a 320 km (200-mile) length of water.2
There are 11 islands with areas greater than 270 square kilometers or 100 square miles in various lakes on Earth.
Each of those islands is large enough to contrain a separate country like a Greek city state or a small tribe.
Wikipedia has a list of recursive islands and lakes. Those are examples where it goes beyond lakes on islands to have islands in lakes on islands, or beyond islands on lakes to have lakes on islands on lakes. Sometimes a step or two farther than that.
So I think that any language in your fictional world is going to need and have separate words for islands and for countries, no matter how common one-island countries may be there.
So in your story characters might travel geogrphically from Drotar Island to Savenal Island to Woen Island to Great Bsodne Island to Endoen Island, and at the same time travel politically from the Republic of Drotar to East Savenal to West Savenal to the Kingdom of Woen to the Bsodne Islands Republic to the Empire of Ten Thousand Islands, for example.
Put a map in the front of the book showing that the countries are in fact all island nations.
Alternately note that while some nations are bigger than others the sea surrounds and separates them all: "In Tlorn we could always see the ocean but in great Thror you could walk for days without seeing the sea." "One could walk around Tlorn's beaches in a day but in Baln the sea cliffs pushed you inland, but never far enough to get away from the sound of the pounding northern surf."
In addition to what people have mentioned re: countries and islands not necessarily being the same even in an archipelago world, another place I would expect to see this show up is world-building. Having everyone live on an island is going to have real consequences for your society/societies. Here are some of the things that come to my mind:
- food: probably involves a significant amount of fish and seafood, and food that can be grown in coastal areas.
- military: having a strong navy (+ air force, depending on your world's tech) is critically important. No marching armies, any inland invasion force needs to get there by ship.
- trade and travel: anything beyond your local region has to go over the ocean. Harbours are the first point of contact and the heart of most cities. Overland travel is never long-distance, which may mean that e.g. roads are not well-planned or maintained.
- professions: Fishers, sailors, shipwrights, navigators, lighthouse keepers, harbourmasters, etc. etc. The status of each profession may also be impacted - e.g. navigators may be highly respected as the point of connection to the outside world.
- art, religion, myth: I'd expect the ocean to play a big role, as well as the history of how the individual country/island developed (were they explorers? were they found, and potentially invaded, by people from another island? did they have a long point in their history where they just thought they were alone in an endless sea? all of these will have a huge impact on the culture)
and so on and so forth.
This is obviously simplistic, especially if some of the islands are bigger, but somewhere to start thinking about how your fictional geography will influence the culture. Also, a powerful thing you can also do here is to have an exception be noted as an exception. Maybe a city in a larger island has a lot of overland caravans arriving... and your POV character finds this really strange and unusual because they've never seen a strong in-island trade network like that, they're used to trade always being done by ship. That says a lot about what the world is like.
If you do this sort of thing, it should be pretty clear to the readers that your society is a strongly ocean-based one and that everyone lives on an island without needing to say so explicitly.