Title is self-explanatory. I know that this question is bit too dumb. But I don't know how to say for sure if a puzzle is enigma or cryptogram. Both of them has a message to decipher. So, finally, What is the difference between enigma puzzle and cryptograms?
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A cryptogram is a puzzle where letters are replaced by some other symbols in a one-to-one cipher. The most common type involves letters being replaced with other letters, but numbers and symbols are also acceptable. So, for instance, A could be replaced with G; B could be replaced with I; C could be replaced with Q; and so on, with random letters chosen and none repeated. The goal of a cryptogram is often to decode the message.
Here is an example of a cryptogram unsolved:
And here is the solution:
You can see that each letter on the bottom corresponds to one letter on the top, and vice versa.
An enigmatic puzzle is one where the solving method is not given. Some great examples of enigmatic puzzles are BmyGuest's "hyper-modern art" series, like this puzzle and this one. They are also common in puzzle hunts such as the MIT Mystery Hunt, ΣUMS, and P&A Magazine.
"Enigmatic puzzles" frequently involve a leap of intuition hinted at through the puzzle's framing; their solutions are usually a common English word or phrase.
Here is an enigmatic puzzle from the 2015 MIT Mystery Hunt:
Even The Blossoming Flowers
Its solution:
The title is the same as the title of a Japanese poem called "Iroha"; it is an alternate ordering for their syllabary. The letters in the grid are laid out in the same way as the syllabary; in this layout, each row represents a consonant (or possibly none) and each column represents the vowel that follows it. If you read off the letters in the order their corresponding syllables appear in the poem, you get the message "PLURAL OF WORD THAT FOLLOWS SHRINK GIFT SANDWICH OR BODY". All of those words are commonly followed by "wrap": "shrink wrap", "gift wrap", "sandwich wrap", or "body wrap". So the answer to the puzzle is "WRAPS".
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$\begingroup$ Some doubts..(1) In the example of cryptogram, english letters were replaced by english letters and in the example of enigma, japanese letters were replaced by english letters. What's the difference then?... (2) Can we call a puzzle cryptogram if no ciphers are used? $\endgroup$– manshuFeb 20, 2016 at 6:54
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$\begingroup$ In a cryptogram, every letter is replaced by some other symbol. If A in the plain text is Q in the coded text, then Q in the coded text always represents A in the plain text. Nothing else is changed. They can be solved by using patterns in English to replace letters and "uncover" more of the plain text. $\endgroup$– Deusovi ♦Feb 20, 2016 at 6:55
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$\begingroup$ In an engimatic puzzle, no instructions are given; the syllables were replaced in this example, but the point was not to find out the replacements. The point was to find some way to get a word or phrase out of it. $\endgroup$– Deusovi ♦Feb 20, 2016 at 6:57
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$\begingroup$ It means that if a puzzle needs cipher and also needs that cipher to be organised then the puzzle will be cryptogram as well as enigma..right? $\endgroup$– manshuFeb 20, 2016 at 7:01
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1$\begingroup$ @manshu: Enigmatic puzzles are not organizing things. Enigmatic puzzles mean that the process and goal are both unclear; you have to figure out what to do. The one I gave you was about organizing things, but not all of them are. The "trick" in that one was to figure out that you needed to reorganize them, then figure out how to reorganize them. Other enigmatic puzzles use very different methods. The thing that links them together is that you have no instructions; both the method and end result are unclear. $\endgroup$– Deusovi ♦Feb 20, 2016 at 7:26