I studied neural networks quite heavily in my first degree in computer science, so I'd argue that neural networks have a very specific meaning, quite clearly defined at
http://en.wikipedia.org/wiki/Artificial_neural_network The disadvantages are that (1) training can take a long time (2) the results are somewhat of a black box, your network will say "buy", "sell", "hold" etc., but it's not clear exactly how it reached that conclusion.Neural networks are a subset of the many tools for machine learning.