Is The Nether randomly generated?

Solution 1:

The nether is just a special Biome, and is generated the same way as any other Biome (except only in the Nether of course). According to the wiki, occasionally nether biomes will spawn in the overworld!

It was a separate map theme in Indev mode (albeit with dirt/sand instead of netherack/soul sand), and as such had a different algorithm for generating the terrain.

So yes, the Nether is randomly generated, it will be different for different seeds (it uses the same seed to generate terrain as the overworld). And even among worlds with the same seed, the location where a new destination nether portal spawns is randomized separately.

Solution 2:

It is generated in the same way as the main world (using the seed). This means it will be different for every world.

If you delete the Nether from the map files and recreate it by taking another portal you will be in exactly the same nether as you were first in.