Physicists use "top" to refer to many different kinds of spinning rigid bodies. The general public also uses it loosely, but in different ways. In this forum, however, it's probably safe to focus on real toy tops meant for use in the real world. I'd require 2 defining attributes: (i) Spinning motion, and (ii) a very high probability of falling over under gravity without spin. I'm on the fence as to whether there should also be (iii) some degree of rotational symmetry about the intended spin axis. (Physicists would call this a "heavy top", or if symmetrical, a "Lagrange top".)
If a real-world top comes to rest without falling over on rare occasion -- say, due to normal tip wear or a convex supporting surface -- I'd still call it a top. But if it did so on a reliable basis, by any means, I'd want to call it something else -- especially if it were designed that way. We recently wondered what to call an otherwise top-like toy that doesn't fall over, but the only consensus reached was that it should be distinguished from a regular top somehow.