Difficulty affects the story in number of different ways. First the game is scaled to be played on Normal for most Hosted Game veterans. When you first choose your difficulty, many things change. First if you choose easy, you start with more attribute points, than you would with Normal, or Hard. Also, on Easy you have 5 checkpoint tokens (or save restores), Normal you only have three, while hard you only have 1. Also, every skill based check, roll, attack, enemy strength / health, depends on the difficulty. On easy, skill checks are easier, normal it is neither easier or harder, and hard make skill checks and combat a little bit more difficult. If you play on hard, you are more likely to die if your ship takes too much damage or you take too much damage. On easy and normal, you have chance to survive and it is a little bit more forgiving if you make a mistake or things go wrong.
Also, the story does change slightly, but mostly in small ways, story content is slightly different, and people interactions may change a little bit, most of them small, but a few slightly bigger, and you may have more or less options in dialogues / choices. The requirement for certain things may be different as well. For example, upgrading your space craft is much easier on easy difficulty than it is on hard difficulty. You may start off with more credits and other resources on easy vs hard. Some achievements you cannot achieve unless you play on Normal or Hard. Certain missions may go differently depending on the difficulty. For example, lets say you play on easy there might only be 1 guard you have to get passed, normal might have 2, and hard might have more or maybe the guards are elite guards.
In terms of just purely story content:
Easy - 98% of the story
Normal - 99% of the story
Hard - 100% of the story.
Mostly it affects skill checks and how challenging the game is.
Depending on your play style here is are some good examples on what difficulty you might choose:
Easy - I just want to experience the story, and though there is combat and skill checks, I don’t want it to be overly difficult. There is still the possibility I could lose, but it is more rare that devastating results would occur.
Normal - I want to experience the story, but I also want combat and skill checks to be challenging. For the most part I should be fine, my character and ship can still be lost, but if I plan well and don’t overextend I should be fine. I can look for challenges if I want and avoid challenges if I want.
Hard - I want to experience the full story and I want everything to be more realistic and in some ways difficult. It shouldn’t be easy to be a Space Captain. I want the ultimate challenge, as it makes the payoff that much more worth it. I understand that even small mistakes can result in devastating consequences, and I need to be careful accepting risking missions unless I know I am ready and prepared for it.
Will the difficulty affect story items such as endings and certain events? The short answer…Yes (the story at times can be slightly different / there are slightly different dialogues), will you notice it (depends on what your doing), the long answer…it might not be super obvious on the main story, but for example when playing the scenarios you might see some major differences and the story in general may add more details / change things when you play on a harder difficulty.