It's not, actually. The actual difference is that beta is a form of B, while Eszett is two letters s (a long one and a short one) joined together and drawn with a single stroke. Alternatively, a letter s and a letter z (hence the name Eszett).
But the context of the question is how a system like a human can make a visual distinction quickly via a characteristic
The characteristic I gave was the little tail which is independent of knowing the derivative of how it got its tail