The word "quine" is now used to refer to two separate concepts - a phrase that quotes itself, and a phrase that reproduces himself. I believe Douglas Hofstadter distinguished these as "self-ref" and "self-rep".

Most self-reps are self-refs. Most self-refs are not self-reps. Additionally, in computer languages, the word "quine" is almost exclusively used to refer to self-reps, even the ones that work by some mechanism other than quining (quoting themselves).

Most of the English sentences above are self-refs, and the computer examples are self-reps. '"preceded by itself in quotes." preceded by itself in quotes.' is both an English quine and a self-rep, because it actually does thoroughly describe itself.

For the sake of comparing what is and is not a self-rep:

  • The Befunge code (this language was selected because it has really short quines) <@,g09,k9"
    This program describes (in fact, it outputs) a certain line of text, which happens to be <@,g09,k9" - which is the same as the code. This is a self-rep. Because it works by making two passes over itself, one of which is in 'quotes', it could be considered a self-ref as well.
  • "preceded by itself in quotes." preceded by itself in quotes.
    This phrase describes a certain phrase, which happens to be "preceded by itself in quotes." preceded by itself in quotes. - which is the same as the phrase. This is a self-ref and a self-rep.
  • 'is not a quine' is not a quine
    This sentence describes a feature of the phrase 'is not a quine'. A sentence is not the same as a feature of part of that sentence. Sure, you could create a sentence which describes that feature. Then, by definition, you get the original sentence or something very similar to it back. "My name is Bob" describes a feature of my name, which is that it is Bob, but in doing so it does not describe the sentence "My name is Bob". So neither does this, in any way, describe the sentence "'is not a quine' is not a quine". So this sentence is a quine, but only by Hofstadter's definition, not by the same definition used for computer programs.
    In fact, I think it would be rather difficult for a complete sentence to be a self-rep. Sentences describe concepts, but sentences are objects. On the other hand, noun phrases describe objects, and noun phrases are objects - noun phrases have a shot at being a self-rep. This is why command-line computer programs can be quines, as well - a command-line computer program's source code describes its output, which is made of lines of text, and a command-line computer program's source code itself is made of lines of text.

I've revised this node after discovering that 'quine' was originally used to mean self-ref and not self-rep. After changing some words, the points before still stand, but the closing statement that I rather enjoyed writing no longer holds:

In summary: "'is not a quine' is not a quine" is not a quine. And neither is the previous sentence.