Answer
All three are damages under the Civil Code but serve different purposes. Moral damages (Article 2217) compensate for non-physical injury such as mental anguish or besmirched reputation, recoverable when they are the proximate result of a wrongful act. Nominal damages (Article 2221) are not compensation at all — they vindicate a right that was violated where no measurable loss was proved. Exemplary damages (Article 2229) are imposed by way of example or correction for the public good, always in addition to another category of damages and never as a matter of right (Article 2233).
A key link runs between them: a plaintiff must first establish entitlement to moral, temperate, or compensatory damages before exemplary damages may be awarded (Article 2234). And for all of these categories, no proof of pecuniary loss is required (Article 2216) — entitlement turns on the legal basis for the award rather than on receipts.