Talking about and referring to Lagrange points can be confusing, since there are Lagrange points in every system in which one celestial body orbits another. So when talking about Lagrange point colonization, one need to specify which system he is referring to.
Republic of Lagrangia is in favour colonizing the 4th or 5th Lagrange point of the Sun-Earth system. Since it’s quite cumbersome to repeat this phrase all over again, we will from now on simply refer to these points as SEL-4 or SEL-5, with SEL standing for Sun-Earth Lagrange point. This system allows us also to easily refer to other Lagrange points: SML for the Lagrange points of the Sun-Mars system, or SJL for the Sun-Jupiter system.
The Main Asteroid Belt (MAB), or simply the Asteroid belt, consists of those asteroids which orbits are between the orbits of Mars and Jupiter. These asteroids are called main belt asteroids (MBA).
There are also asteroids outside the MAB. Those asteroids which orbits are (at least partially) within the orbit of Mars are called Near Earth Asteroids (NEA).
Trojan asteroids are asteroids which have been trapped into a system’s L4 or L5. Most famous are the Jovian Trojans, but also Martian, Neptunian and Terrestrial Trojans have been discovered. Especially the last are of particular interest, since a population of Terrestrial Trojans will provide the mineral resources needed to build space habitats and for export to Earth.
At this moment the existence of one Earth Trojan Asteroids has been confirmed, but scientists believe more Earth Trojans should exist.
A space habitat is a space station designed for hosting a permanent population of a substantial size. Space habitats, also known as space settlements, are located in free space as opposed to colonies on or under the surface of a celestial body. When we talk about space colonization, we mean the creation of space habitats.