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Suppose I meet somebody on Monday morning; when I am departing, I say "See you later."
Does that mean I will see again that person during the day?
If that is what would be understood, what should I say when I am not sure when I am going to see again that person?
No, 'see you later' simply means at a time that is later than now.
You are more likely to use differentiation in the opposite situation, i.e. when you know you will be seeing someone at a certain time. In those instances you could use variants such as:
See you later this afternoon.
See you later tonight.
However, you wouldn't use this if the next time you were to see the other person is beyond today, so 'See you later tomorrow' or 'See you later next week' wouldn't work.
No, it doesn't imply anything but "So long". It's just a standard formulaic valediction when departing, much as "Hi, how're you doing?", a standard formulaic salutation when first meeting, implies nothing but "Hello": it's not a real question.
OTOH, if you normally see the valedictorian later in the day most days, say, for coffee or lunch or dinner, then it might mean something specific to you, and if you won't be free, you probably will want to say something about that.
