The starting spells are added based on your character's major skills.
If you have different major skills for different character, then you'll get different starting spells.
Yep,
There is also a (reasonably) well known glitch where spell tome spells randomly add themselves to your spell book without you ever having read the book, this can happen when you fast travel or (I think) load a game, basically randomly.
So it could well be this as well if they aren't the normal base spells you get.
EDIT: So I just properly read through your post (sorry, I was being lazy), and yep, they're just the ones you get added by proxy if you choose certain Magic Schools as majors: Serenity would be from illusion, and Minor Respite is one you get automatically, even if you choose no magic schools.
EDIT 2: My mistake, I was confusing Heal Minor Wounds with Minor Respite. I've never heared of Minor Respite being automatically added, so it could well be a Spell Tomes glitch.