Enigma, n.; pl. Enigmas.
Etymology: [L. aenigma, Gr.
1. A dark, obscure, or inexplicable saying; a riddle; a statement, the hidden meaning of which is to be discovered or guessed. A custom was among the ancients of proposing an enigma at festivals. Pope.
2. An action, mode of action, or thing, which cannot be satisfactorily explained; a puzzle; as, his conduct is an enigma.
Shades of meaning
Fernald has no entry of its own for enigma; he lists it under riddle.
Where he writes about it:
Conundrum, a word of unknown origin, signifies some question or statement in which some hidden and fanciful resemblance is involved, the answer often depending upon a pun; an enigma is a dark saying; a paradox is a true statement that at first appears absurd or contradictory; a problem is something thrown out for solution; puzzle (from oppose) referred originally to the intricate arguments by which disputants opposed each other in the old philosophic schools. — from riddle
Both enigma and puzzle may be applied to any matter difficult of answer or solution, enigma conveying an idea of greater dignity, puzzle applying to something more commonplace and mechanical; there are many dark enigmas in human life and in the course of providence; the location of a missing object is often a puzzle. — from riddle