This question is rather difficult to phrase.
I played a character to lvl 9, then left them alone. Then I played a different character to 15, advancing further in the quests and storyline.
Today I logged into my old lvl 9 character, and all the quests I completed on Character 2 showed as completed and my next quest was way up in lvl 15sville.
Are storyline quests shared across characters? There's no way to have a character separate from that (aside from "going back" on Character 1 and "starting" at an earlier quest in the line)?