neural networks are seperate, they are built purely to learn and my assumption is that heuristics are rules that are learnt, expert systems are purely built with lots of facts (like a database) and able to draw a conclusion from hueristics
you notice how heuristics is like a 'rule' for both, its hard to generally define it, but specifically in AI, expert systems its alot easier to
if you do the 2004 HSC paper there is a question asked similar to what you're saying, look at the answer as well you'll notice CTA uses heurstics as an example for heurstics to draw conclusion with expert system of medical diagnosis