In-game, you have two types of nebulae: "normal" nebulae, which are large, irregular in shape and don't have a star associated with their centre. Planetary/Supernova-remnant nebulae are smaller, symmetrical and have an end-life star of some kind (eg. Wolf-Rayet, S class, neutron star, black hole, etc) in their centre.
Hot, bright stars (mostly O-types) can also have little fuzzy "nebulae" attached to them, which are visible on the Galaxy map but aren't named and aren't visible anywhere else except on the Galmap. These are the blobs you can often see form a distance as you scroll the map around, especially with map filters set to deselect all stars.
Note that some in-real-life supernova remnant nebulae are portrayed in ED as normal nebulae, simply because they're too big to portray as remnants. The Crab Nebula an the Veil Nebulae come to mind.
Final fact: out there in the real universe, nebulae are lit up for a reason: usually, a hot bright star (or a bunch of such stars) nearby. There are probably plenty more nebulae out there that we can't see, simply because there's no bright stars in them, just like a streetlight in a forest will light up the nearby trees, but leave the rest of the forest in darkness. The "dark nebulae" that we do know about, like the Coal Sack, are only visible to us because they happen to be sitting in front of a large patch of bright stars, so it's blocking out their light.
In ED, it was considered too difficult to create "proper" lightsourcing for nebulae, so they are just magically lit up all by themselves. Real-world nebulae are often placed in-game alongside the real-world stars that should be making them light up, though sometimes the distances don't quite match up (like Eta Carinae and the Eta Carina Nebula, which in-game are 1000 LYs apart), but of course the procedurally-generated nebulae lack any such real-world stars. Many of the large, bright, procedurally-generated nebulae, such as the Traikaae Nebula, are far away from any bright stars that could be making them light up like that.