Fog of war means that you can only see on the map what is within your scanning range.
The original Ferion had a sort of fog of war where you needed to just discover a star system and everything will be known to you, all the time. This was logical to do with the hardware limitations we had back in the day, real fog of war would have been expensive to calculate.
Using scanners, planets and ships both have scanners. Planet scanners are usually more powerful and used to detect incoming enemies. Ship scanners allow you to discover enemy fleets, planets, wormholes etc.

The dotted circles around your ships/planets indicate their scan range
From the start of the game, you will be able to see all the stars on the map. Planets will remain visible on your map after you have discovered them. However, the information of that planet (who owns it, if its destroyed etc) is from the last time you visited it.
Other players ships are only visible if they are within active scan range.

The H indicates that your information about this planet is outdated
Discovering planets requires a ship with scanners. Usually players fly around the star in a circle to find most of the planets. Once you have one settled planet in a solar system, its scanners will pick the other planets in most cases.

Command your scouts to fly around the star to find the planets
You can also hire a minister called Vorn to enhance your scanning capabilties. With him, flying to the star of a solar system automatically reveils all planets in that system.

Vorn of the ministry of exploration