Chaotic doesn't mean crazy, and has been misnamed forever (lawful too). The Lawful/Chaotic axis is the divide between community and individualism. To use a real work example, on the social-political charts it would be listed as authority vs anarchy (or authoritarianism vs libertarianism, but that's considered loaded).
Elves, as chaotic good, encourage the individual freedom of each elf. If an elf's needs or desires is outside of the group's norm, it's not shunned (so long as it's not evil, which is the other axis). They tend to be selfish, but not to the point of evil. This does mean that organizing the community is harder, but major issues (such as defense) will still be resolved quickly.
Orcs, as chaotic evil, care far more about themselves than each other. It's assumed that an orc's needs or desires is outside of the group's norm, so that is the norm. Organizing almost requires a strong leader to overcome their innate selfishness (and often cowardice, since they'd rather run away than die with the group).
In both cases the individual is more important than the group, but the good/evil access often determines the specifics. A strong leader in a chaotic soceity would ease organization, but isn't necessary. An elf could still be cowardly and an orc could still be foolishly brave, but the good/evil axis tends to color things (good cares about good, while evil feeds upon itself).