Is an ellipsis a distinct punctuation mark?
Solution 1:
The Chicago Manual of Style has this to say about an ellipsis, and the use of ellipsis points or suspension points to indicate the presence of an ellipsis (emphasis mine):
13.48 Ellipses defined
An ellipsis is the omission of a word, phrase, line, paragraph, or more from a quoted passage. Such omissions are made of material that is considered irrelevant to the discussion at hand (or, occasionally, to adjust for the grammar of the surrounding text).
Chicago style is to indicate such omissions by the use of three spaced periods (but see 13.51) rather than by another device such as asterisks. These points (or dots) are called ellipsis points when they indicate an ellipsis and suspension points when they indicate suspended or interrupted thought (see 13.39). They must always appear together on the same line (through the use of nonbreaking spaces, available in most software applications), along with any following punctuation; if an ellipsis appears at the beginning of a line, any preceding punctuation (including a period) will appear at the end of the line above.
If they prefer, authors may prepare their manuscripts using the single-glyph three-dot ellipsis character on their word processors (Unicode 2026), usually with a space on either side; editors following Chicago style will replace these with spaced periods.
From a typographer's perspective, there's another reason to prefer three spaced periods:
To add the ellipsis punctuation mark to text, hit Option-semicolon (Mac) or Alt-0133 (Windows). You can also create an ellipsis by typing three periods. The advantage of this method is that you can alter the spacing of the dots using tracking, which is particularly useful when a font's ellipsis appears too tight or too open. In most fonts, the ellipsis is made from three periods, but the spacing of these periods can vary from font to font.
Solution 2:
It is a distinct punctuation mark, yes. It's not a matter of correct grammar though, but orthography.
The widespread equivocation of the triple-period and ellipsis arose because typewriters had a limited selection of glyphs and typists were taught to use three periods to compose an ellipsis. This persists in manuscript and screenplay format standards. Prior to the typewriter, either a single piece of movable type could be used for the ellipsis or a set of three full stops with appropriate spacers; today it can be directly input with some systems such as those of Macs and iPhones.
What method of composition is "correct" is a matter of house style and will vary by the typesetter and publisher. Most existing style manuals recommend spaced periods. Because of the way HTML automatically wraps words three un-spaced periods might get broken across lines, so one is forced to use either spaced periods with non-breaking spaces or the Unicode ellipsis character to achieve an indivisible ellipsis.
Neither a triple-period (spaced or unspaced) or a precomposed ellipsis is more correct than the other, but regardless of how it is composed, the ellipsis is still a distinct punctuation mark even when it it is composed of multiple characters.