Corporations are the grouping structure of employees and are a logical path for players interested in the merchant path of play or in research and development. Corporations can be joined or formed with little effort, though raising in rank and power requires considerable effort. Companies can acquire other companies via take over or partnership and can own structures, though cannot govern regions of space.
Companies can morph into factions; in fact many factions are also companies or own companies, and in so doing they can take ownership of regions of space. Companies may also form fleets, issue contracts and hire/fire employees to boost their capabilities, or trim back their overhead respectively.
Corporation story factors vary depending on the company’s activities; companies can play an active but indirect role in faction politics and may also manipulate hunters and criminals alike making company gameplay the most versatile in terms of story affect. It is of note that companies will have to participate at some degree with hunters, criminals and factions in order to grow, though smaller companies can be maintained as a means to fuel a more adventure like mode of game play without the need of a faction or story driven paths.
Business makes the galaxy go around ... not really, it's the draw of gravitational fields but you get the idea.