Difference between NFA and NBA
It's impossible to tell if all you have is the pictorial representation, since these look the same for both types of automata. Even if you're given a formal specification you won't necessarily be able to tell the difference (it depends on how these automata are encoded).

This kind of ambiguity is similar to linguistic ambiguity that can occur in real life. For example, suppose you see the word "impossible" written on the wall. Can you tell whether it's English or French?

Sometimes this kind of ambiguity is purposeful. For example, the pictorial representation of a DFA doubles as the pictorial representation of an equivalent NFA. The only difference in your case is that the two interpretations are inequivalent.