How do elastics work?

What is the difference between the bonds in a rubber band and that in say candle wax that make the elastic stretchy and the candle not?

Cross links between the individual polymer molecules. See http://en.wikipedia.org/wiki/Crosslinked_polymer for more.

So would a hard plastic have lots of cross links, a rubber band less and wax, none at all?

That doesn’t really tell the whole story; many crosslinked polymers show little or no elasticity. It’s how they’re crosslinked that matters. An elastic polymer, like most polymers, has molecules that resemble long strands. Before crosslinking, these strands tend to be coiled or tangled, like spaghetti. During crosslinking (an effect usually produced by chemical reaction and heat), the cross links form between regions of the polymer that are adjacent at the time – but when you pull on the material, the strands straighten, and the cross links come under strain. When you release the tension, the cross links pull the strands back into their coiled configuration.

Crosslinking between relatively straight molecules produces films or gels, or even hard solids, depending on how many links are formed, and where, and in what environment.

Hard waxes tend to be partly crystalline, although that doesn’t cover all of it.

Nametag didn’t mention it, so I will. Many thermoset polymers (like the ones I work with) are densely cross-linked. Anything “fiberglass” or “carbon fiber”- the plastic part of the thing is cross-linked. Irreversibly so.

Also, a rubber band does not stretch forever. When the strands completely uncoil and reach their maximum length the rubber band becomes fairly stiff. At this point the rubber acts like most materials. Pull on a rubber band until it it fully streched out. After that it can still take quite a bit more stress with little additional elongation.