According to the Chicago Manual of Style (my go-to style guide),
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.
I am sure almost every style guide will specify that ellipses are three-period marks, which makes every instance you've encountered of the notorious two-period mark … just a typo. ;)