No Man’s Sky is not as focused on realism as Elite : Dangerous, the planets are at fixed points within the system. The resources used to fuel your ship in NMS are found on asteroids and planets.

In earlier versions the sun was a part of the skybox rather an object within the gameworld, so it couldn’t actually be visited, which you can now do with this new update. Haven’t tried it myself, but from what i have heard it takes somewhere between 5 and 15 minutes to get there (probably depending on how upgraded the impulse drive, this games equivalent of supercruise, is) from the systems hyperspace exit. Should drop you out of impulse at a certain distance, planets and other points of interest do that too. Getting too close deals constant damage to your ship.