It is customary in mathematics, philosophy, linguistics, academia, etc., to use single quotes to indicate the word itself, and double quotes to indicate opague context.
The word 'dog' has three letters.
The word 'dog' is "mentioned" in the above sentence.
The word 'mentioned' in the above sentence is used in the technical philosophical sence which distinguishes between "use" and "mention".
When I talk about someone, and I use his name, I mention him.
Long ago I advocated that the general semantics community adopt the convention that is standard in the greater community. On the Use of Quotation Marks,. I recently added some research here.
With respect to words and the above conventions:
Single quotes direct the reader to the word itself - the object level prior to any extended semantic reaction.
No quotes (the default) direct the reader to the conventional referent of the word - to the semantic reaction brought forth as the "meaning" of the word.
Double quotes direct the reader to an awareness of opague context - to higher levels of abstraction in which secondary and higher level alternative semantic reactions are brought forth.
I conform to these conventions for the most part. With respect to the particular variety of opague context which we deem requires use of the extensional device, I add double or "scare" quotes. I'll put double quotes around most uses of the 'is' of identity, and I will generally put these "scare" quotes around any references to the event level, but I usually qualify those by adding the word 'putative'. I will also sometimes follow the convention that the use a verbal indicator of mention allows dropping the single quotes.
"'Four' has four letters" means the same as "the word four has four letters". (Mentioned by quote, mentioned by using the word 'word'.)
Single quotes take us down a level of abstraction.
Double quotes take us up a level of abstraction.
I don't think of quotation marks as having a noun-like definition, but they do function as an instruction as to how to interpret the enclosed text. That makes them different from adjectives or adverbs, which modify not the text, but the referent of the text.
I would not call them an "undefined term", as they are not terms, but punctuation marks.