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It's a sample sentence in Google Dictionary:
run along
phrasal verb of run
1.informal
go away (used typically to address a child).
"run along now, there's a good girl"
synonyms: go away, be off (with you), shoo; More
Do it mean "If you go away now, you are (still) a good girl"?
Or "You'd better hit the road now, especially when/because there's a good girl (somewhere else) waiting for you"?
"Run away" and "run along" may seem similar but are used quite differently. The difference is idiomatic. Your question title says one but the body of your question asks about the other, so I will address both.
Run away is self explanatory. It means to depart (at speed) from something, because "away" is a relative direction meaning anywhere but here.
Run along is an idiom which is an order to leave, not in any particular direction, but "along" implies that the person continue with their other business.
Your example:
"run along now, there's a good girl"
I would describe this as quaint British English and would expect to see it in period literature, either said to a little girl by an elder as a way of asking her to perhaps go and play elsewhere; or perhaps said to someone older as way of patronising them. The implication is that they are behaving, or being a "good girl" by following the order to go away.
In this instance "there" is not used as a direction, but as a sort of introduction, the way you might say "there's somebody at the door".
In essence it means,
I am asking you to leave and, as you are a good girl, I expect you to do so.
According to Cambridge Dictionary
used to show approval or encouragement
It matches your first idea:
If you go away now, you are a good girl
