Four different narratives or frames can be identified in the current phase of terraformation of Mars.
Mars through Science
This is the most classical approach of Mars, and mostly fuelled by curiosity towards Mars itself - most Mars-centric. Its primary aims are to understand the geological process of planet-forming and to research the possibilities extraterrestrial life.
Humans, plants and animals are refugees that seek sanctuary on Mars to ensure the continuation of earth originated life in the case of events of mass extinction on Earth like nuclear warfare, ecological breakdown, the eruption of a super-volcano or a hit with a large asteroid.
Mars is the site for the next stage of technology-driven human evolution, that would be too dangerous on Earth. Mars is the perfect site to project the emergence of the genetically and technologically enhanced post-human.
In this narrative, Mars is an economic driver, in the midst of an enormous (potential) wealth, floating in space in the form of mineable asteroids. As raw ores on Earth are all but depleted, various private companies are set up to to mine the asteroids and other celestial bodies. Funded by investment capital mainly from Silicon Valley, the underlying narrative is that of expanding Earth's economy over the solar system.