Is it a different storyline with different bosses, similar to the difference between Normal and Hard Mode Dungeons?
or is it the same storyline, and same bosses, just more difficult, like Normal/HM/Extreme Primals?
I'm asking, because I am probably never, ever going to be a Savage raider. for the most part, I dont have the skill nor the patience to deal with it, and I'd just like to know if I am going to miss out on any important storyline by only doing Normal Raids.
It's just a difficulty bump.
AT this time there is no different storyline for savage, you just go in and clear. However, it has been hinted that they are considering having a different storyline for savage in 4.0 that would differ from the "normal" mode. Whether they actually will or not... /shrug
The fights are more difficult. Things tend to hit harder/have more health than the normal/story mode counterparts.
Some times there may be different/added mechanics to the Savage fights compared to normal fights. For example: A11N has telegraphed AOEs/attacks where as A11S does not have telegraphed AOE markers. Both versions of Sophia have the tilts, but the tilts are far more forgiving in the Hard Mode version.
Savage fights usually have an Enrage mechanic that happens sooner than a normal mode counterpart (if the normal mode has an Enrage).
I'm sure there's more differences, but these are ones I can think of off the top of my head. Generally, Savage doesn't have a storyline of its own.
Difficulty, more mechs, better gear.
That's about it.
I think the story in general for Savage raids has been that the wandering minstrel over in Mor Dhona retells the story of the raid... With a few additions for dramatic effect.