There are currently five different factions in No Man's Sky, each with distinct languages, lore, and technology.
While the Sentinels serve as a police force and are of unknown origin or true intentions, the three main factions (Korvax, Gek and Vy'keen) inhabit the star systems.
The Korvax are a near-immortal sentient machine species. They value science and exploration. They also worship the Atlas and accept the Sentinels' presence. They specialize in Exosuit technology.
The Gek are a sentient amphibious species. They value commerce, and the ancient First Spawn Gek believed themselves to be the master race of the galaxy. They specialize in Starship technology.
The Vy'keen are a humanoid sentient species. They are military-oriented with a very rigid honour system and a deep hatred for Sentinels. They specialize in Multi-tool technology.
The Travellers are a mysterious humanoid species of free explorers that recently arrived in the galaxy. Their origins and purposes are unknown.
The Anomalies are a mysterious humanoid species and each of them wear helmets, hiding their true appearance. Their origins and purposes are unknown.
You can be affiliated with the first three factions mentioned above, but your reputation with e.g. the Korvax won't affect your reputation with the other factions because they are not hostile to each other. However you cannot have any reputation with the Sentinels, the Travellers or the Anomalies.