"The woman runs after the boy."
Translation:Kvinnan springer efter pojken.
Does this mean that the woman runs after the boy temporally, or that the woman chases the boy?
It could mean either. But for chasing, you might use the verb jaga instead (which literally means hunt): Kvinnan jagar pojken.
I've seen "after" spelled two different ways: "efter" and "after." I was wondering if there was a difference or maybe my friend made a typo when he was texting me. It just occurred to me that this sentence could mean that the boy runs before the woman or that the woman is chasing the boy.
It's only "efter", I don't believe "after" is even a word in Swedish. Your friend must've made a typo.
As annika_a already explained, it can mean both of the things you suggested.