In general, there isn’t a unique definition for the multiplication of one vector by another, but there are several common “vector products”, such as the dot product and the cross-product.
The dot product of the two vectors (x, y, z) and (a, b, c) is ax + by + cz.
I kinda assumed that in ICE, the Multiply node would give me the same result, but it turns out that Multiply gives (ax, by, cz):
eX-SI 
The real difference is that in dot product you end up with a scalar. While ICE multiplies to quantities of same type to end up giving the same kind. Which in this case would be a 3D vector and hence you get three values.
While a cross product of two 3D Vectors yields a 3D Vector.
Yup. That’s what my screenshot shows 😉