I would have thought a serif was just a plain ol’ serif, but you can find them in many many ways because they have a classification and features of their own. For example, serifs can be bilateral, unilateral, reflexive, transitive, slab, bracketed, abrupt, wedged, rounded, hairline, squared, etc.
Let's take a look at some of this serifs characteristics:
A bracket is a curved connection between the serif and the main form of the character. Not all serifs are bracketed serifs, and the shapes can be very different: You can either find very intense curves, or very soft and gentle lines, but it sure changes the way a font looks.
Bilateral serifs are the ones that extend to both sides of the main stroke.
Hairline serifs are recognisable for being much thinner than the main strokes of a character, they are common on modern style serifs.