Jesus uses three different Greek terms that are translated as "world" in one version or another of the Gospels. However the word "world" of , but that concept captures none of them precisely. One, kosmos, describes the word as human society. Another, ge, describes the world as the planet. The third, aion, describes the word as "the current era".
These words usually occur in the singular. Sometimes these words appear with an article "the", but sometimes they don't. Unfortunately, Biblical translation adds articles or subtracts them regardless of the Greek. Those distinctions are not currently covered here, though they are being explored for a future addition to this article.
The World Order, Kosmos
The most common one is kosmos. It is usually translated as "the world" in the KJV and most other English translations. The Greek kosmos is very different than the English word, cosmos. The English word refers to the universe, but the Greek word does not describe Carl Sagan's cosmos. In Greek, cosmos means "the world," but it specifically means the world of people. It means society, civilization, and the political powers and divisions of that world. This is the kosmos of the English word, cosmopolitan, which combines the kosmos with the polis, the Greek word meaning "city."
Jesus uses the word in the Greek sense, the world of people. More to the point, the kosmos is the man-made world, the artificial world. It includes not only the physical products, our cities, and our tools, but also our man-made culture: our ideas, our sciences, and so on. Jesus uses this word to describe the archetype of the male aspect of civilization, the one that becomes corrupt and oppressive. He tells those who challenge him, "You are of the world; I am not of the world (Jhn 8:23)." He says this challenging the way they think and see the world, that is, their cultural and intellectual viewpoint.
In some cases, it also seems as though Jesus uses cosmos to refer specifically to the Roman rule of the world. During his era, Rome dominated the known world. When Jesus refers to an "era" (see below), he may sometimes also be referring to the Roman era and its duration.
The Planet, Ge
Christ also uses another word to describe our planet. That word ge. In archetypical terms, this is the positive feminine force of nature that is used by mankind. The Greek word is feminine. This word is usually translated as "the earth" in the KJV Bible but occasionally as "the land" and "the ground." It also refers to the "dirt". In Greek, it refers to the earth as mother, the world of nature. Ge is the God-made world, the planet. Jesus describes this as the potentially productive aspect of nature. Many of his parables refer to using it productively.
The two terms, the world and the earth, are often interchangeable in English. They are not interchangeable in the Greek of Christ's words. Most translation respect this fact. When you see the word "world" in any mainstream translation, the Greek source is kosmos . When you see "earth" or "Earth," the source is ge.
The Era, Aion
Also translated as world is aiôn, which means "lifetime", "life", "a space of time", "an age," an epoch," and "the present world." This word is important because it is translated as "world" in phrases referring supposedly to the "end of the world" (see this article on that concept). However, it is also translated as "world" when the fancy strikes, such as in Luke 16:8, where it is used in the phrase "the children of this world". This word is, however, translated in a huge variety of ways including "age", "forever" and so on.
What Christ Says About the World and the Earth
Christ says very different things when talking about kosmos and talking about ge. He never says that he came to earth (ge). He always says that he came into the world (kosmos). He speaks in the world (Jhn 16:28 et al). It is the world into which children are born (Jhn 16:21). He and his followers are the light of the world (Jhn 12:46 and Matthew 5:14). It is the world that rejoices (Jhn 16:20) and hates (Jhn 7:7). Every idea he expresses about society, the good and the bad, he attributes to "the world," that is, the kosmos.
Christ says much less about the planet, ge. He says that the meek shall inherit the earth. Whenever he talks about "heaven" in relationship to the planet, he uses ge. The word for sky is masculine and the word for earth or ground is feminine so they represent the two basic aspects of the universe. When he talked about the earth passing away, he talks about ge. Christ will be lifted up from the planet, not human society (Jhn 12:32). This is contrasted with a seed the must fall into the planet and die to produce fruit (Jhn 12:24).
To see a clear contrast between his two use of the term, look at Matthew 5:13. where he talks about "the salt of the earth" and the following verse, Matthew 5:14, where he talk about "the light of the world." In both, he is addressing his followers. In the first, he is talking about their natural wit. In the second, he is talking about what they know that human society doesn't know.