Do you remember the terror of waking after a nightmare alone? That would be my answer to the last part of your question.
Regarding night terrors in general, there are a lot of theories about what causes them (and nightmares in general), but that doesn't lend itself very helpfully to what to do to alleviate them.
Nightmares are emotionally-difficult dreams (and night terrors are the same thing, only 1/2 awake and capable of movement throughout, rather than sleep-paralyzed which is normal for dreams of all kinds) that are just a part of the brain re-ordering itself and coping with the issues of the day.
There are two things I found really helped and recommend to others in dealing with night terrors: a change of temperature (open a window, turn on a fan, a cold cloth on the forehead, etc.) and a really, really stupid question. Asking the child something stupid and obvious has a remarkable way of pulling them 'back to reality' very quickly. Things like 'am I your dad? (or for dads, 'mom' <G>)' or 'what colour are your eyes, honey?' seem to work, as do 'is your pillow a rock?' or 'is your bed made out of marshmallow?' Sometimes the question has to be repeated a few times to re-direct their attention, but it works.
The other thing I found helpful, particularly late in the evening when the children are getting ready for bed (apart from ensuring they never watch broadcast news or violent tv or movies or video games -- violent images make a mess of sleep) is talking about what dreams are, and how it is possible to interact with them, be aware of them, and change what's happening in them.
"Make the monster into a blue fluffy bunny" was my eldest daughter's advice to her little sister, years and years ago. It was the plan she'd come up with to deal with a chasing monster in her dreams, years before. I didn't realize she'd remembered it.
Dreams are just imagination, and while we are sleeping we are asleep --not unconscious-- and can have influence and awareness of our dreams, just as we have awareness of our body in space, which keeps us from falling out of bed or rolling onto our bedmates.
It helps to talk about it right before and right after sleep, in that 'nearly groggy' state, because at those times, the unconscious mind is more open to suggestions.