Curly quotation marks curve or slant inward toward the content they bracket. (The font or typeface choice determines how they look, precisely.) Straight quotation marks are… straight. Word can do either, but you have to set your preference.
Click the little pilcrow on the Home ribbon in Word to see all the behind-the-scenes formatting marks that make documents look good. But what are those marks? See the table for a list.
In some versions of Word, these symbols are grey or black.
